Answers
STEP - BY - STEP EXPLANATION
What to find?
• The system of equation of the argumented matrix.
,• The resultant after the given row operations.
Given:
The system of equation is:
7x - 7y + z = -5
3x - 3y + 8z = -5
-6x + y + 3z = 7
Hence, the correct option is D
The following row operations are to be performed;
[tex]\begin{gathered} R_1=-2r_2+r_1 \\ \\ R_3=2r_2+r_3 \end{gathered}[/tex]The first row operation implies that you will multiply row 2 by -2 and then add to row. The resultant gives a new row 1.
This means that the elements in row 1 becomes:
Row 1 : 1 -1 - 15 | 5
Row 2: 3 -3 8 | -5
As for row 3, we will multiply row 2 by 2 and then add to row 3 to get a new row 3.
That is;
Row 3 : 0 -5 19 | -3
ANSWER
Option D
Part B
[tex]\begin{bmatrix}{1} & {-1} & {-15\text{\mid}} & {5} \\ {3} & {-3} & {8\text{ }}| & {-5} \\ 0{} & -5{} & {19\text{ }|} & {-3} \\ {\placeholder{⬚}} & {\placeholder{⬚}} & {\placeholder{⬚}} & {\placeholder{⬚}}\end{bmatrix}[/tex]1 -1 - 15 | 5
3 -3 8 | -5
0 -5 19 | -3
Related Questions
What feature of Kelth's graph makes it difficult to visually compare the responses of those with some college to those shown in the other graphs? (Select all that apply.) (A)The donut hole in the graph made by Keith is a different size than in the graphs made by Ramon. (B)The graphs do not have data labels showing the percentages.(C)The graphs made by Keith and Ramon are all donut pie charts. (D)The graphs made by Keith and Ramon compare groups across education level. (E)The graphs made by Keith and Ramon use the same colors for each of the corresponding responses. 2 How would you change Keith's graph for easier comparison? (Select all that apply.) (A) Make all donuts exactly the same size, with the radius of the holes the same as well. (B)Change the graphs from donut ple charts to time series graphs. (C)Use different sets of colors in each of the donut ple charts.(D)Combine the graphs into one donut pie chart.(E) Add data labels showing the percentages,
Answers
Answer:
(A)The donut hole in the graph made by Keith is a different size than in the graphs made by Ramon.
Explanations:
Ex
Considering the graph made by Keith and those made by Ramon, we would observe that Keith's graph ( Some college) has a smaller donut hole that Ramons's graphs ( High school or less, and college graduate). This difference in the donut holes will make any comparism made between the " some college" graph and other graphs to be inaccurate.
PROGRESSIVEKayla ForshaeSupervisor: "Our goal is to make add-on sales during 85% of sales. If you make 35sales, how many add-on sales do you need to make to meet the goal?"
Answers
We are given that the total number of sales is 35.
According to the question, his goal is to make add-on sales during 85% of sales.
Therefore, the add-on sales would be:
[tex]\Rightarrow\frac{85}{100}\times35=29.75\approx30[/tex]Hence, we will need to make 30 add-on sales to meet the goal.
12)If the legs of a right triangle are 6 cm and 5 cm, find the area of the triangle.A)11 cm2B)15 cm2C)30 cm2D)60 cm2
Answers
Determine if the figures below are similar. If they are, identify the similarity statement.E70F50GK5060L
Answers
We have the following triangles:
And we need to determine if they are similar by identifying the similarity statement.
To determine that similarity statement, we can proceed as follows:
1. Check the measures of the internal angles of the triangles. We need to remember that the sum of the internal angles of a triangle is 180 degrees. Then we have:
2. We can see that to find the angles in the first triangle, EFG, and in the second triangle, JKL, we have that the sum of the three angles must be 180 degrees, and we obtained the other angles as follows:
[tex]\begin{gathered} \text{ Triangle EFG}\rightarrow50+70+x=180 \\ \\ x=180-(50+70)=180-120=60 \\ \\ \text{ Triangle JKL}\rightarrow50+60+y=180 \\ \\ y=180-(50+60)=180-110=70 \end{gathered}[/tex]3. Then we can redraw the triangles as follows:
4. Now, since we can see that, at least, two of the angles of the triangles are congruent (then the third one is also congruent, that is, has the same measure), we also have that to prove that if two triangles are similar it is sufficient that two of the corresponding angles of one triangle are congruent to the two corresponding angles of the other triangle, and this is known as the Angle-Angle method for proving similar triangles, then we can conclude that:
Triangle EFG is similar to triangle JKL by the Angle-Angle method.
Therefore, in summary, we have that:
Triangle EFG is similar to Triangle JKL by Angle-Angle similarity
[tex]\text{ Triangle EFG \textasciitilde Triangle JKL by Angle-Angle similarity}[/tex]
[Last option]
The height of a triangle is 3 m
more than twice the length of the
base. The area of the triangle is
76 m2. Find the height of the triangle. Help me!
Answers
The triangle has a height of 19 meters.
How to determine the height of a triangle
In this problem we find the area of a triangle, in square meters, and the relationship between its height (h) and its base length (b), both in meters. We must solve the following expression to determine the height:
A = (1 / 2) · b · h
h = 3 + 2 · b
A = 76
Then,
76 = (1 / 2) · b · (3 + 2 · b)
152 = b · (3 + 2 · b)
152 = 3 · b + 2 · b²
2 · b² + 3 · b - 152 = 0
Finally, we find the roots of the polynomial by quadratic formula:
b₁ = 8, b₂ = - 19 / 2
Since, lengths are non-negative real numbers, the only possible solution is b = 8 and the height of the triangle is:
h = 3 + 2 · 8
h = 19
The height of the triangle is 19 meters.
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Im confused on what you have to do in order to find the answer
Answers
Given:
The ship is moved from (-10,9) to (-1,-5) in the coordinate plane.
To find:
The transformation rule
Explanation:
The initial point can be written to obtain the terminal point as follow,
[tex](-10+9,9-14)\rightarrow(-1,-5)[/tex]In general,
We write,
[tex](x,y)\rightarrow(x+9,y-14)[/tex]Final answer: Option C.
[tex](x,y)\operatorname{\rightarrow}(x+9,y-14)[/tex]
Find an equation of the line, and write it in (a) slope-intercept form if possible and (b) standard form.
Answers
1) Note that we need to find a perpendicular line. Perpendicular lines have reciprocal and opposite slopes. So we know that the slope we need is -3
2) We also know that it must pass through (-2,-6), so let's plug the slope -3 the point (-2,-6) so that we can find the linear coefficient:
[tex]\begin{gathered} y=mx+b \\ -6=-3(-2)+b \\ -6=6+b \\ -6-6=b \\ b=-12 \end{gathered}[/tex]
in a dog show there are 31 dogs competing in the terror group the top three dogs with we'll all wind crash price of $500 and moved on to complete for a place in the larger Best in Show competition how many ways can the top three dogs be determined if they are finishing position is not important
Answers
The selection of three dogs out of 31 dogs can be done in
[tex]31C3\text{ ways}[/tex]i.e.
[tex]\begin{gathered} =\frac{31!}{(31-3)!\times3!} \\ =\frac{31\times29\times28!}{28!\times3!} \\ =\frac{31\times29}{6} \\ =149.8 \\ \cong\text{ 150} \end{gathered}[/tex]HELP PLEASEEEEEEEE!!!
Answers
The rational number is -91/100 or -0.91.
What is Rational number?Any number of the form p/q, where p and q are integers and q is not equal to 0, is a rational number. The letter q stands for the set of rational numbers.
The word "ratio" is where the word "rational" first appeared. Rational numbers are therefore closely tied to the idea of fractions, which stand for ratios. In other terms, a number is a rational number if it can be written as a fraction in which the numerator and denominator are both integers.
Given:
We have to find the rational number between -0.45 and -0.46
Now, make both decimal into fraction
-0.45 and -0.46
-45/100 and -46/100
Now, multiply 2
-45/100 x 2/2 and -46/100 x 2/2
-90/100 and - 92/100
Hence, the rational number is -91/100 or -0.91.
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The rational number is -91/100 or -0.91.
What is Rational number?Any number of the form p/q, where p and q are integers and q is not equal to 0, is a rational number. The letter q stands for the set of rational numbers.
The word "ratio" is where the word "rational" first appeared. Rational numbers are therefore closely tied to the idea of fractions, which stand for ratios. In other terms, a number is a rational number if it can be written as a fraction in which the numerator and denominator are both integers.
Given:
We have to find the rational number between -0.45 and -0.46
Now, make both decimal into fraction
-0.45 and -0.46
-45/100 and -46/100
Now, multiply 2
-45/100 x 2/2 and -46/100 x 2/2
-90/100 and - 92/100
Hence, the rational number is -91/100 or -0.91.
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What’s is the volume and surface area of the figure shown ?
Answers
• The total surface area of a cylinder is given by:
[tex]SA=2πr\left(r+h\right)[/tex]where r = 1.75 cm
h = 3 cm
Hence:
[tex]SA=2\times\pi\times1.75\times(1.75+3)=57.7\text{ }cm^2[/tex]• The volume of a cylinder is given by:
[tex]V=πr^2h[/tex]Hence:
[tex]V=\pi\times(1.75)^2\times3=28.9\text{ }cm^3[/tex]ANSWER
surface area = 57.7 cm²
volume = 28.9 cm³
An employee makes $10.59 per hour but is getting a 4% increase. What is his new wage per hour to the nearest cent?
Answers
In order to calculate the new wage per hour, we just need to multiply the old value of $10.59 by 1.04, that is, an increase of 4%, so we have:
[tex]10.59\cdot1.04=11.01[/tex]So the new wage per hour is $11.01.
The hands of a clock show 11:20. Express the obtuse angle formed by the hour and minute hands in radian measure.
Answers
ANSWER
[tex]2.44\text{ }rad[/tex]EXPLANATION
First, let us make a sketch of the clock:
We have that for a minute hand:
[tex]1\text{ }min=6\degree[/tex]For hour hand:
[tex]1\text{ }min=0.5\degree[/tex]The hour and minute hand have their origin at 12.
At 11:20, the minute hand had moved 20 mins. This means that:
[tex]20\text{ }min=20*6=120\degree[/tex]The hour hand had moved at 11 (and 20 mins more), which means:
[tex]\begin{gathered} 11*60\text{ }min+20\text{ }min \\ \Rightarrow660\text{ }min+20\text{ }min \\ 680\text{ }min \end{gathered}[/tex]Hence, in 680 mins:
[tex]\begin{gathered} 680*0.5 \\ \Rightarrow340\degree \end{gathered}[/tex]Therefore, the angle formed between 11 and 12 at 11:20 is:
[tex]\begin{gathered} 360-340 \\ \Rightarrow20\degree \end{gathered}[/tex]Hence, the angle formed at 11:20 is:
[tex]\begin{gathered} 120\degree+20\degree \\ 140\degree \end{gathered}[/tex]Now, let us convert to radians:
[tex]\begin{gathered} 1\degree=\frac{\pi}{180}rad \\ 140\degree=140*\frac{\pi}{180}=2.44\text{ }rad \end{gathered}[/tex]That is the obtuse angle formed in radians.
3.In the figure. What are the coordinates of the image of point B after a translation (x+4, y-7) ?
Answers
Answer:
(5, -5)
Explanation:
The coordinate of Point B is: (1,2)
If we carry out the translation (x+4, y-7) on point B, we have:
[tex]B(1,2)\rightarrow (1+4,2-7)=B^{\prime}(5,-5)[/tex]The coordinates of the image of point B is (5, -5)
when you isolate the variable, what must you do to keep the equation balanced x-3=7?
Answers
Answer:
To isolate the variable, we have to add 3 to both sides of the equation to keep the equation balanced.
So x = 10
Explanation:
Given the below equation;
[tex]x-3=7[/tex]To isolate the variable, we have to add 3 to both sides of the equation to keep the equation balanced;
[tex]\begin{gathered} x-3+3=7+3 \\ x=10 \end{gathered}[/tex]A study found that 36% of the assisted reproductive technology (ART) cycles resulted in pregnancies. Twenty-six percent of the ART pregnancies resulted in multiple births. (a) Find the probability that a random selected ART cycle resulted in a pregnancy and produced a multiple birth. (b) Find the probability that a randomly selected ART cycle that resulted in a pregnancy did not produce a multiple birth.(c) Would it be unusual for a randomly selected ART cycle to result in a pregnancy and produce a multiple birth?
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
assisted reproductive technology (ART) cycles:
pregnancies = 36%
pregnancies resulted in multiple births = 26%
Step 02:
a.
p (pregnancies) = 36% = 36/100 = 0.36
pregnancies resulted in multiple births = 26% = 26/100 = 0.26
p(pregnancies resulted in multiple births) = 0.36*0.26 = 0.0936
b.
p (pregnancy did not produce a multiple birth) = 1 - 0.0936 = 0.9064
c.
Indeed, the probability of multiple pregnancies is low 9.36%.
That is the full solution.
A circle has a center point at the coordinates P(3,0) with a diameter line RT where R has the coordinates (-47,25).What is the Coordinates Of T
Answers
Given: A circle has a center point at the coordinates P(3,0) with a diameter line RT where R has the coordinates (-47,25).
Required: To determine the coordinates of T.
Explanation: The given circle is-
Let the coordinates of T be (x,y). Then the center of a circle is divided by the diameter in the ratio of 1:1. The section formula for a point (x,y) dividing a line segment in the ratio of 1:1 is-
[tex]\begin{gathered} x=\frac{(x_1+x_2)}{2}, \\ y=\frac{(y_1+y_2)}{2} \end{gathered}[/tex]Hence, for the given line RT, point P divided RT in 1:1. Thus-
[tex]\begin{gathered} 3=\frac{-47+x}{2}, \\ 0=\frac{25+y}{2} \end{gathered}[/tex]Further solving for x and y as-
[tex]\begin{gathered} x=6+47 \\ \Rightarrow x=53 \\ and\text{ }y=-25 \end{gathered}[/tex]Final Answer: The coordinates of T are (53,-25).
Determine the domain and the range of the function.C. Determine where the function is increasing and where it is decreasing.
Answers
Given:
[tex]f(x)=2x^2-x+1[/tex][tex]a=2\text{ ; b= -1 ; c=1}[/tex]Graph opes upwards.
Let the vertex be (h,k)
[tex]h=-\frac{b}{2a}[/tex][tex]h=-\frac{(-1)}{2(2)}[/tex][tex]h=\frac{1}{4}[/tex][tex]k=f(h)[/tex][tex]k=2(\frac{1}{4})^2-\frac{1}{4}+1[/tex][tex]k=2(\frac{1}{16})-\frac{1}{4}+1[/tex][tex]k=\frac{1}{8}-\frac{1}{4}+1[/tex][tex]k=\frac{1-2+8}{8}[/tex][tex]k=\frac{7}{8}[/tex][tex]\text{Vertex}=(\frac{1}{4},\frac{7}{8})[/tex]Axis of symmetry is
[tex]x=\frac{1}{4}[/tex]y- intercept
x=0,
y=1
There is no x intercept .
Domain:
[tex](-\infty,\infty)[/tex]Range:
[tex]\lbrack\frac{1}{4},\infty)[/tex]The function is increasing:
[tex](\frac{1}{4},\infty)[/tex]The function is decreasing:
[tex](-\infty,\frac{1}{4})[/tex]
Find the derivatives of the following using the different rules.1. f(x) = -67x
Answers
To derive f(x) = -67x, we can use the Power Rule.
[tex]x^n\Rightarrow nx^{n-1}[/tex]In the given term, our n = 1 since x¹ = x. So, following the power rule, we will multiply the exponent 1 to the constant term -67, then subtract 1 from the exponent 1, hence x¹ will become x⁰.
[tex]-67x^1\Rightarrow1(-67)(x^{1-1})[/tex]Then, simplify.
[tex]-67x^0\Rightarrow-67(1)=-67[/tex]Therefore, the first derivative of f(x) = -67x is -67.
[tex]f^{\prime}(x)=-67[/tex]A loaf of bread is cut into slices size. Some of the loaf us used in a recipe and 4/8 of the loaf is used to make a sandwich. The remaining 2/8 of the loaf is put into the remaining
Answers
We have
[tex]\frac{7}{10}-\frac{2}{10}[/tex]in order to know what expression is equivalent, we need to solve and simplify the expression above
[tex]\frac{7}{10}-\frac{2}{10}=\frac{5}{10}=\frac{1}{2}[/tex]Then we will solve the next expressions in order to find the equivalent expression
[tex]undefined[/tex]The flow of water from a faucet can fill a 4-gallon container in 28 seconds Give the ratio of gallons to seconds as a rate in gallons per second and as a reduced fraction. The faucet fills the container at rate of——gallon per second
Answers
The flow of water can fill a 4-gallon container in 28 seconds.
Given:
Number of gallons = 4
Time = 28 seconds
Hence, the ratio of gallons to seconds will be 4 : 28
[tex]\begin{gathered} As\text{ a rate in gallons per second = }\frac{\text{number of gallons}}{time\text{ taken}} \\ As\text{ a rate in gallons per second = }\frac{4}{28}=\frac{1}{7} \\ As\text{ a reduced fraction, the rate in gallons per second is }\frac{1}{7}\text{gallons per second} \end{gathered}[/tex]Therefore, the faucet fills the container at the rate of 1/7 gallon per second
Evaluate : g(x) = x^2 + 4x ; find g(2)
Answers
Given the function
[tex]g(x)=x^2+4x[/tex]We want to evaluate this function at x = 2.
When we evaluate a function at a given value, we just need to substitute the terms with a variable by the given value.
[tex]g(2)=(2)^2+4\cdot(2)=4+8=12[/tex]HElP
pls pretty pls its due today
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Answers
The equation of the line in slope intercept form is y = -2x - 70
How to find the equation of a line?The equation of a line can be represented in different form such as slope intercept form, point slope form and standard form.
The equation of the line can be written is slope intercept form as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, using the coordinates (0, - 70)(-20, -30)
Let's find the slope,
m = slope = -30 + 70 / -20 - 0
m = 40 / - 20
m = - 2
Let's find the y-intercept using (0, -70)
-70 = -2(0) + b
b = - 70
Therefore, the equation of the line is y = -2x - 70
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Pete Corporation produces bags of peanuts. Its fixed cost is $18,200. Each bag sells for $3.43 with a unit cost of $1.83. What is Pete’s breakeven point?
Answers
Let's call x to the bags of peanuts. One bag has a variable cost of $1.83, then the variable cost of x bags is 1.83x dollars.
The total cost of production for the corporation is obtained by adding fixed and variable costs. In this case, the total cost is 18,200 + 1.83x dollars.
The revenue for the corporation of 1 bag is $3.43, then of x bags is 3.43x dollars.
When the revenue and the total cost are equal, the breakeven point is reached, in this case:
18,200 + 1.83x = 3.43x
18,200 = 3.43x - 1.83x
18,200 = 1.6x
18,200/1.6 = x
11375 = x
The cost of production of 11375 bags is:
Total Cost = 18,200 + 1.83*11375
Total Cost = 18,200 + 20816.25
Total Cost = 39016.25
Pete’s breakeven point is (11375, 39016.25), or, 11375 bags and $39,016.25
Spilt each number into its prime factors. Please enter the prime factors from smallest to largest.84 =
Answers
Let's make the table of the prime factors of 84:
then we have that 84=2x2x3x7, therefore, the prime factors are 2, 3 and 7
x + y = 5 y - 2x = -4
Answers
x = 3, y = 2
Explanations:The equations are:
x + y = 5......................(1)
y - 2x = -4...................(2)
Make x the subject of the the formula
x = 5 - y...............(3)
Substitute equation (3) into equation (2)
y - 2(5 - y) = -4
y - 10 + 2y = -4
3y = -4 + 10
3y = 6
y = 6 / 3
y = 2
Substitute the value of y into equation (3)
x = 5 - 2
x = 3
52. What is the 275th digit after the decimal point in therepeating decimal 0.6295 ?F. 0G. 2H. 5J. 6K. 9
Answers
Given:
The digit is 0.6295.
Required:
To find the 275th digit after the decimal point in the repeating decimal 0.6295.
Explanation:
For any non-negative integer, we have:
The 4n+1th digit after the decimal point is 6.
The 4n+2th digit after the decimal point is 2
The 4n+3th digit after the decimal point is 9
The 4n+4th digit after the decimal point is 5.
Since the repeating digit is 4 and we have to find the 275th digit.
Thus
[tex]\frac{275}{4}=68\text{ with remainder 3}[/tex]It can be written as:
275 = 4. 68 + 3
That is 275th digit after the decimal point in the repeating decimal is 9 with n= 68.
Final answer:
Thus option k is the correct answer.
Which type of statically graphic uses bars to describe the data ?Dot plot Box plot Histogram
Answers
HISTOGRAM
Explanations:
Data are reported using visuals to make reporting easier and ease the understanding of the audience.
Some of the graphic used in statistics to report data and make inference include:
• Bar charts
,• line charts
,• Dot plot
,• Box plot
,• Histogram etc.
Bar charts and histograms make use of bars to report data. This charts are important to detect outliers that may be present in our data.
We can therefore conclude that the type of statically graphic that uses bars to describe data is the HISTOGRAM
Four friends participated in a free contest for charity. Erin scored 4 less points than Taylor. Nya scored three times as many points as Erin. Aaron scored 10 more points than Nya. Together the four friends scored a total of 158 points. Find how many points each friend made :How many points Taylor scored :Erin scored : Nya scored :Aaron scored:
Answers
Taylor's scored 22 points
Erin scored 18 points
Nya scored 54 points
Aaron scored 64 points
Explanation:Let Taylor's point = x
Erin scored 4 less points than Taylor:
Erin's score = x - 4
Nya scored three times as many points as Erin:
Nya's score = 3(x - 4)
Aaron scored 10 more points than Nya:
Aaron's score = Nya's score + 10
= 3(x - 4) + 10
The total score of the four friend = 158 points
Taylor's score + Erin's score + Nya's score + Aaron's score = 158
x + (x - 4) + 3(x -4) + 3(x-4) + 10 = 158
Expand the parenthesis:
x + x -4 + 3x - 12 + 3x - 12 + 10 = 158
collect like terms:
x + x + 3x + 3x - 4 - 12 - 12 + 10 = 158
8x - 18 = 158
8x = 158 + 18
8x = 176
Divide both sides by 8:
8x/8 = 176/8
x = 22
Taylor's scored 22 points
Erin scored : x-4 = 22- 4 = 18 points
Nya scored : 3(x-4) = 3(22-4) = 3(18) = 54 points
Aaron scored: 3(x-4) + 10 = 54 + 10 = 64 points
show the prime factorisation of 49 :-;
thankyou.
Answers
Answer:
The prime Factorization of 49 is 7.7
Step-by-step explanation:
Hope this helps! :))
Answer:
7
Step-by-step explanation:
The factors of 49 are 1, 7, and 49
Solve the following simultaneous equation using the inverse matrix method
3x + 4y = 18
4x - y = 5
Answers
The values of x and y obtained by inverse matrix method are 2 and 3 respectively
What is an inverse matrix?An inverse of a matrix, A, is a matrix [tex] A^{-1}[/tex], that multiplies matrix A to give an identity matrix.
The inverse matrix method involves defining and making use of a coefficient matrix, A, a variable matrix, X, and a constant matrix, B, which are obtained from the system of equations as follows;
A·X = B
The system of equations is presented as follows;
3·x + 4·y = 18
4·x - y = 5
From the above system of equations, we have:
[tex]The \ coefficient \ matrix, \ A = \begin{bmatrix} 3&4 \\ 4& -1 \end{bmatrix}[/tex]
[tex]The \ variable \ matrix, \ X = \begin{bmatrix} x \\ y \end{bmatrix}[/tex]
[tex]The \ constant \ matrix, \ B = \begin{bmatrix} 18 \\ 5 \end{bmatrix}[/tex]
From the equation, A·X = B, we have;
[tex]\therefore X = \dfrac{B}{A} = A^{-1} \times B[/tex]
Where: A⁻¹ is the inverse matrix of A, which is found as follows;
[tex]If\ A = \begin{bmatrix} a&b \\ c&d \end{bmatrix}[/tex]
[tex]Then, \ A^{-1} = \dfrac{1}{a\cdot d-b\cdot c} \cdot \begin{bmatrix} d& -b \\ -c& a \end{bmatrix}[/tex]
Which gives the value of A⁻¹ obtained from the coefficient matrix, A = [tex]\begin{bmatrix} 3&4 \\ 4& -1 \end{bmatrix}[/tex] as follows;
[tex]A^{-1} = \begin{bmatrix} 3 & 4 \\ 4 & - 1 \end{bmatrix}^{ - 1} = \dfrac{1}{(3 \times - 1) - (4 \times 4)} \times \begin{bmatrix} - 1 & - 4 \\ - 4 & 3 \end{bmatrix}[/tex]
[tex]A^{-1} = \dfrac{1}{(3 \times - 1) - (4 \times 4)} \times \begin{bmatrix} - 1 & - 4 \\ - 4 & 3 \end{bmatrix} = \begin{bmatrix} \dfrac{ - 1}{ - 19} & \dfrac{ - 4}{ - 19} \\\\ \dfrac{ - 4}{ - 19} & \dfrac{3}{ - 19} \end{bmatrix}[/tex]
The variable matrix, [tex]X = A^{-1} \times B[/tex], which gives the value of the variables in the solution is therefore;
[tex]X = \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} \dfrac{ - 1}{ - 19} &\dfrac{ - 4}{ - 19} \\ \\\dfrac{ - 4}{ - 19} &\dfrac{3}{ - 19} \end{bmatrix} \times \begin{bmatrix} 18 \\ 5 \end{bmatrix} = \begin{bmatrix} 2 \\ 3 \end{bmatrix}[/tex]
[tex]\begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 2 \\ 3 \end{bmatrix}[/tex]
Therefore;
x = 2 and y = 3
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