Solve system of equations.
x+y=-6
2 x-y=3

Answers

Answer 1

The system of equations involving x + y = -6 and 2x - y = 3 has the solution x = -1 and y = -5.

A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.

There are three methods that can be used to solve system of linear equations.

1. Elimination

2. Substitution

3. Graphing

Using substitution method, given two linear equations in x and y,

x + y = -6     (equation 1)

2x - y = 3     (equation 2)

Express y in terms of x in one of the equations,

x + y = -6     (equation 1)

y = -x - 6

and then substitute it in the 2nd equation.

2x - y = 3     (equation 2)

2x - (-x - 6) = 3

2x + x + 6 = 3

3x = 3 - 6

3x = -3

x = -1

Substituting the value of x in the equation of y,

y = -x - 6

y = -(-1) - 6

y = 1 - 6

y = -5

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Related Questions

Figure B is a dilated image of figure A. What is the scale factor?

Answers

Demarcus

Explanation:

7:40pm------What is 89 minutes more? (What time will it be?)

Answers

The current time is 08 : 09 pm

How to determine the current time?

The given parameters are

Time = 7 : 40 pm

Minutes added = 89 minutes

The current time is calculated as

Current time = Time + Minutes added

So, we have

Current time = 7 : 40 pm + 89 minutes

Evaluate the sum

Current time = 7 : 129 pm

Rewrite properly as

Current time = 08 : 09 pm

Hence, the current time is 08 : 09 pm

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The fairs train ride covers a distance of 3 miles in 20 minutes what is the speed for the ride in miles per minute​

Answers

Answer:

0.15 miles per minute or 9 miles per hour

Step-by-step explanation:

PLS HELP ASAP!!!! WILL GIVE BRAINIEST!!!!!! 100 POINTS!!!!!

SEE ATTACHED PIC

Answers

Answer:

y-coordinate

Step-by-step explanation:

x-intercepts lie on the x-axis. On the x-axis, y=0 while the x value is changing.

Answer: Set the Y equal to zero and solve for x

Step-by-step explanation:

four less than the product of 2 and a number g

Answers

The expression that represents the statement "four less than the product of 2 and a number g" is 2 g - 4.

We are given a statement:

four less than the product of 2 and a number g

We need to form an expression to represent that statement.

An expression is a combination of variables and constants by using the various operations of mathematics like addition, subtraction, division and multiplication.

So, first we will find the product of 2 and a number g.

This is:

2 × g = 2 g

Now, we will subtract 4 from the expression:

2 g - 4

Therefore, the expression that represents the given statement "four less than the product of 2 and a number g" is 2 g - 4.

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According to government tests, a late model hybrid car gets 45 miles per gallon of gas. If gasoline sells
at $3.20 per gallon, how many miles will the car travel on $20.00 of gas?

Answers

since we already know 45miles per gallon which is $3.20 per gallon so, we will multiply 45miles with $20 of gas that would equal to 900miles.
The car will travel 900 miles on $20.00 of gas.

AB=2x+7,AC=7x-3,BC=4x-2

Answers

The value of x on the line segment is 8

How to determine the value of x?

The given parameters are:

AB = 2x + 7

AC = 7x - 3

BC = 4x - 2

The above means that the point B is on the line segment AC

So, we have:

AC = AB  + BC

This gives

2x + 7 + 4x - 2 = 7x - 3

Evaluate the like terms

-x = -8

Divide both sides by -1

x = 8

Hence, the value of x on the line segment is 8

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Which expression is equivalent to −30+(−40)+(−70) ?


−(30−40)+(−70)
negative open parenthesis 30 minus 40 close parenthesis plus open parenthesis negative 70 close parenthesis

30 + 40 + 70
30 + 40 + 70

−30+(−70)+(−40)
negative 30 plus open parenthesis negative 70 close parenthesis plus open parenthesis negative 40 close parenthesis

−30−(40−70)

Answers

The answer choice which correctly represents an equivalent expression to that which is given as in the task content is; −30 + (−70) + (−40).

Which expression is equivalent to that which is as given in the task content?

It follows from the task content that the expression whose equivalent is to be determined is; −30 + (−40) + (−70).

Therefore, since it follows from the associative property of addition that;

a + b + c = a + c + b.

Therefore, same can be said for the expression as given in the task content where;

-30 + (-40) + (-70) = -30 + (-70) + (-40).

Ultimately, the required equivalent expression is; −30+(−70)+(−40); negative 30 plus open parenthesis negative 70 close parenthesis plus open parenthesis negative 40 close parenthesis

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Harry tosses a nickel 4 times. The probability that he gets at least as many heads as tails is.

Answers

When a nickel is being tossed 4 times, there will be 16 possible outcomes:

HHHH, 0 tails and 4 heads

HHHT, 1 tails and 3 heads

HHTH, 1 tails and 3 heads

HHTT, 2 tails and 2 heads

HTHH, 1 tails and 3 heads

HTHT, 2 tails and 2 heads

HTTH, 2 tails and 2 heads

HTTT, 3 tails and 1 heads

THHH, 1 tails and 3 heads

THHT, 2 tails and 2 heads

THTH, 2 tails and 2 heads

THTT, 3 tails and 1 heads

TTHH, 2 tails and 2 heads

TTHT, 3 tails and 1 heads

TTTH, 3 tails and 1 heads

TTTT, 4 tails and 0 heads

Eleven of these outcomes have a head-to-tail ratio of at least one head for every two tails. Therefore, there is an 11/16 chance of getting at least as many heads as tails.


Mai-Lin measures her heart rate whenever she exercises and tries to make sure that she is staying in her target heart rate zone. The American Heart Association suggests a target heart rate of T=0.75(220-a), where T is a person's target heart rate and a is his or her age.
b. If Mai-Lin's target heart rate is 153, then how old is she? What property justifies your calculation?

Answers

When Mai-Lin's target heart rate is 153, then her age is 16 years.

How to illustrate the function?

From the information, the The American Heart Association suggests a target heart rate of T=0.75(220-a),

where T = person's target heart rate

a = his or her age.

Therefore, when the heart rate is 153, the age will be:

T = 0.75(220 - a)

153 = 165 - 0.75a

0.75a = 165 - 153

0.75a = 12

Divide

a = 12/0.75

a = 16

The person's age is 16 years.

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the function g is defined as followed

g(x)=2x^2-7

if the graph of g is translated vertically downward by 3 units, it becomes the graph of a

function h

FIND THE EXPRESSION FOR h(x)


(If you know how to answer these questions please help with the next 2 or three I will post afterwards)

Answers

Since the graph of g is translated vertically downward by 3 units, the graph of function h is equal to h(x) = 2x² - 10.

The types of transformation.

In Mathematics, there are different types of transformation and these include the following:

ReflectionRotationTranslationDilation

What is a translation?

A translation can be defined as a type of transformation which moves every point of the object in the same direction, as well as for the same distance.

Since the graph of g is translated vertically downward by 3 units, the graph of function h would be represented by the following expression:

Note: g(x) = 2x² - 7

h(x) = g(x) - 3.

h(x) = 2x² - 7 - 3.

h(x) = 2x² - 10.

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A janitor had 2/3 of a spray bottle of cleaning solution. He used 1/6 of a solution of the day .How much does a bottle did he use?

Answers

Answer:

3/6

Step-by-step explanation:

2/3 = 4/6

(multiply 2 by 2 = 4, multiply 3 by 2 = 6)

4/6 - 1/6 = 3/6

Answer:

2x2/3x2-1/6

4/6-1/6=3/6=1/2

he used half for the day

hope this helps or may also he correct •-•

a radioactive substance decays exponentially. a scientist begins with 180 milligrams of a radioactive substance. after 33 hours, 90 mg of the substance remains. how many milligrams will remain after 43 hours?

Answers

The radioactive substance remaining after 43 hours is: 62.7273 mg by unitary method.

What is unitary method?

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method.

Now,

Given that 180 mg is present at t = 0 hours.

After t = 33 hours, substance left = 90mg

By unitary method, after = 1 hour, substance left = [tex]180-\frac{90}{33}=180 -\frac{30}{11}[/tex]mg

The substance left after t = 43 hours = [tex]180 - \frac{30\times43}{11}= 180 - \frac{1290}{11}=180 - 117=62.7273mg[/tex]

Hence, The radioactive substance remaining after 43 hours is: 62.7273 mg by unitary method.

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Find the missing terms in the sequence.

4, 6, 10, 16, 24, 34, __, 60, 76, __, 114

Enter the two missing terms with only a comma between them.

Answers

Answer:

46, 94

Step-by-step explanation:

hope this works for you :)

Ava and Wyatt are reading the same book. At the beginning of the month, Ava was on
page 10 and Wyatt was on page 30. Ava will read 20 pages per day and Wyatt will
read 15 pages per day. Let A represent the page of the book that Ava is on at the end
of t days into the month, and let W represent the page of the book that Wyatt is on at
the end of t days into the month. Graph each function and determine after how many
days, t, Ava and Wyatt will be on the same page of the book.

Answers

Ava and Wyatt will take 4 days to be on the same page of the book.

X-values must be chosen and entered into the equation in order to graph a function. You will obtain a y-value once those values have been entered into the equation. A single point's coordinates are made up of its x and y values.

From the given question we can get:

A = 10 ₊ 20t

W = 30 ₊ 15t

Graph the each function to get the number of days.

A function can only be graphed if X-values are selected and put into the equation. Once those values are introduced into the equation, a y-value will be produced. The values of x and y are the coordinates of a single point.

Hence we get the number of days as 4. and the graph is attached below.

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The vertices of ABCDE are A(-6, 0), B(-3, 0), C(0, -3), D(-3, -6), and E(-6, -3). Find the vertices
of the image after a translation using the rule (x,y) → (x + 9, y - 6) and a dilation with a scale
factor of 1/3 centered at the origin.

Answers

The coordinates of the image of the vertices of the polygon are A''(x, y) = (1, - 2), B''(x, y) = (2, - 2), C''(x, y) = (0, - 1), D''(x, y) = (- 1, - 2) and E''(x, y) = (- 2, - 1).

What are the images of the vertices of a polygon by using rigid transformations?

Rigid transformations are transformations applied on geometric loci such that Euclidean distances in such constructions are conserved. Translations and dilations are common examples of rigid transformations.

If we know that A(x, y) = (- 6, 0), B(x, y) = (- 3, 0), C(x, y) = (0, - 3), D(x, y) = (- 3, - 6) and E(x, y) = (- 6, - 3), then the coordinates of the image are determined below:

Translation

A'(x, y) = (- 6, 0) + (9, - 6)

A'(x, y) = (3, - 6)

B'(x, y) = (- 3, 0) + (9, - 6)

B'(x, y) = (6, - 6)

C'(x, y) = (0, - 3) + (9, - 6)

C'(x, y) = (9, - 9)

D'(x, y) = (- 3, - 6) + (9, - 6)

D'(x, y) = (6, - 12)

Dilation

A''(x, y) = (1 / 3) · (3, - 6)

A''(x, y) = (1, - 2)

B''(x, y) = (1 / 3) · (6, - 6)

B''(x, y) = (2, - 2)

C''(x, y) = (1 / 3) · (0, - 3)

C''(x, y) = (0, - 1)

D''(x, y) = (1 / 3) · (- 3, - 6)

D''(x, y) = (- 1, - 2)

E''(x, y) = (1 / 3) · (- 6, - 3)

E''(x, y) = (- 2, - 1)

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The temperature in California was 105 on Thursday. The temperature in the North Pole was -20. What is the difference between the two temperatures.

Answers

The answer is 125 degrees. Hope this helped! :)

Answer:

125

Step-by-step explanation:

105 - (-20) = 105 + 20 = 125

Marco earns a commission rate of 6% for
the first $6,500 ins sales and 9% on sales
over $6,500. Find the total graduated
commission on sales of $10,500.

Answers

Total graduated commission earned by Macro on sales of $10,500 with the rate of 6% on the first $6500 and 9% on sales over $6500 is equal to $750.

As given in the question,

Macro earns commission rate of 6% for the first $6500

And 9% on sales over $6500

Out of $10,500

For first $6500 Commission =(6500 × 6)/ 100

                                            = $390

For $ (10,500 - 6,500 = 4000) commission = (4000 × 9)/ 100

                                                                   = $360

Total graduated commission on sales of $10,500 = $( 390 + 360)

                                                                             = $750

Therefore, total graduated commission earned by Macro on sales of $10,500 with the rate of 6% on the first $6500 and 9% on sales over $6500 is equal to $750.

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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
(14+3)(2
x 6)

Answers

Answer: 204

Step-by-step explanation:

(14+3)(2 x 6)=

(17)(2 x 6)=

(17)(12)=

17*12=

17*(10+2)=

17*10+17*2=

170+34=204

Answer:204

Step-by-step explanation:

Members of a sports club are junior, adult
or senior.
80 of these members were asked whether
they prefer tea, coffee or hot chocolate.
25 members are senior, of which 13
prefer coffee.
10 juniors prefer tea.
There are no adult members who prefer
hot chocolate.
2 out of the 18 juniors prefer coffee.
4 out of the 28 members who prefer tea
are seniors.
What fraction of members in the club
prefer hot chocolate?
Give your answer as a fraction in its
simplest form.

Answers

Fraction of members in the club that prefer hot chocolate = [tex]\frac{7}{40}[/tex]

It's Given that :

A sports club has 80 participants.

Senior Members = 25

Junior Members = 18

Adult Members = 80 - (25 + 18) = 80 - 43 = 37

JUNIOR MEMBERS :

Prefers tea = 10

Prefers Coffee = 2

Prefers hot chocolate = 18 - (10 + 2) = 18 - 12 = 6

SENIOR MEMBERS :

Prefers tea = 4

Prefers coffee = 13

Prefers hot chocolate = 25 - (4 + 13) = 25 - 17 = 8

ADULT MEMBERS :

Prefers tea = 28 - (10 + 4) = 28 - 14 = 14

Prefers coffee = 37 - 14 = 23

Prefers hot chocolate = 0 (none)

Calculation of Fraction of members in the club that prefer hot chocolate = 8 + 6 = 14 members out of 80 members

= [tex]\frac{14}{80} = \frac{7}{40}[/tex]

Therefore 7 / 40 of members prefer hot chocolate.

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proof let a be a square matrix of order n. (a)show that is symmetric. (b)show that is skew-symmetric. (c)prove that a can be written as the sum of a symmetric matrix b and a skew-symmetric matrix c, a

Answers

(a)Symmetric matrix -

Let matrix A be of order 3×3 =

                                  [tex]\left[\begin{array}{ccc}1&3&8\\3&8&-4\\8&-4&6\end{array}\right][/tex]

So, the transpose of A will be -

A' =

                                  [tex]\left[\begin{array}{ccc}1&3&8\\3&8&-4\\8&-4&6\end{array}\right][/tex]

So, we can say that A=A'. So, it is symmetric.

(b) Skew - symmetric matrix -

Let us consider a matrix B =

                                  [tex]\left[\begin{array}{ccc}0&-6&4\\-6&0&7\\4&7&0\end{array}\right][/tex]

matrix B is said to be skew-symmetric if aij =−aji.

(B' =−B)

B'  =    

                                 [tex]\left[\begin{array}{ccc}0&6&-4\\6&0&-7\\-4&-7&0\end{array}\right][/tex]

(c) A + A′ is a symmetric matrix for any square matrix A with real number entries, whereas A - A′ is a skew-symmetric matrix.

Proof: If B = A + A', then B ′ = (A + A ) ′

(A + B)′ = A′ + B′, thus = A′ + (A′)′

(as (A′)′ =A) = A′ + A

= B (because B + A = B + A′)

B = A+A′ is a symmetric matrix as a result.

Let C now equal A-A′.

Why does C' equal (A-A′)′=(A′)′?

= A′ - A (Why?)

=- (A - A′) = - C

A - A′ is a skew-symmetric matrix as a result.

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Help I will Mark A Brainlist !!!! Its A Math Question Find the length of a.

Thank you ao much !!! I hope you have a good day!

Answers

I believe your answer is C
Trust

Answer: a=2√5

Step-by-step explanation:

We have a right-angled isosceles triangle

Hence, a=2√5

Pls help I’ll give Brainliest

Answers

Answer: I hope this helps.

Step-by-step explanation:

Find the Error A large box of spaghetti noodles contains 3 pounds and costs $2.40. A student said the unit cost is $1.20 per pound. Complete the statement to explain why the student was incorrect and find the correct answer.

Answers

Answer:

1.25 a pound

Step-by-step explanation:

if it was 1.20 per pound it would be less money

Choose the correct statement.
-2 < -3
1 = -1
5 > -6

Answers

The answer is only 1

each side of the base of a right octagonal prism is 7 in. long. the altitude of the prism measures 12 in. find the lateral area.

Answers

The lateral area of  right octagonal prism = 672 in^2.

Which octagonal prism is appropriate?

An example of a prismatic uniform polyhedron is the octagonal prism, or op. There are 2 octagons as well as 8 squares in it. Each vertex connects two squares and one octagon. As the name implies, it is an octagonal-based prism.

Describe a 3D figure.

Three-dimensional geometry is a solid figure, item, or shape comprising three dimensions—length, breadth, as well as height.. Three-dimensional structures have height, which is equivalent to thickness or depth, unlike two-dimensional shapes.

According to the given data:

Solve for lateral surface area:

altitude = 12

base = 7

AL=8ah

Putting the value we get:

AL=8 * 12 * 7

Al = 672 in^2

the lateral area of  right octagonal prism = 672 in^2.

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You play a game on your phone. For every correct move you make, you receive 50 points. For every second that it takes you to complete the game, you lose 3 points. You complete the game in 2 minutes 24 seconds using 35 correct moves. What is your score?

Answers

You get 1750 points from the 35 correct moves (35 x 50) and you get -432 points from time taken (144 x -3) therefore you end the game with 1318 points.

1318 Points.

A jug contains 3/4 pints of orange juice. After you pour 5/8 of a pint into a glass, how much is left in the jug?

Answers

Answer:

1/8

Step-by-step explanation:

Help please I will give brainliest

Answers

Answer:

For sure, A and C. However, I cannot fully read the last one.

Step-by-step explanation:

Be sure to mark me Brainliest!

a basket contains 3 types of fruit. The apples weigh 4/9 kilogram, the oranges weigh 1/6 kilogram, and the pears weigh 5/18 kilogram. What is the total weight of the fruit in this basket?

A) 10/33
B)15/18
C)8/9

Answers

The answer is C

Make all of the denominators common

4/9 x 2 = 8/18

1/6 x 3 = 3/18

5/18

8/18 + 3/18 + 5/18 = 16/18

When you simplify you get 8/9
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