Question

What is the solution to this system of equations?

3x + 2y = -10

y = -x - 4


A. (-2,-2)

B. (-2,2)

C. (-18,14)

D. No solution

Answer 1

Answer: Choice A

(-2, -2)

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Step-by-step explanation:

I'll use the substitution method to solve this system.

Replace y in the first equation with -x-4. This is because y = -x-4 is mentioned in the second equation.

So,

3x + 2y = -10

3x + 2( y ) = -10

3x + 2( -x-4 ) = -10 .... substitution

3x - 2x - 8 = -10

x - 8 = -10

x = -10+8

x = -2

Then use this to find y

y = -x-4

y = -(x) - 4

y = -(-2) - 4

y = 2 - 4

y = -2

We have x = -2 and y = -2 pair up together

They form the ordered pair solution (x, y) = (-2, -2)

This shows why Choice A is the answer.

Another way to see this is to graph each equation given using a tool like Desmos. It's a free graphing app.

See below.

The two lines intersect at (-2, -2) which is the solution.

Answer 2

3x + 2y=-10 equation 1

y=-x -4 equation 2

use the substitution method of elimination to get the answer to the question.

*using substitution

substitute equation 2 in one and we get

3x +2(-x-4)=-10

3x- 2x-8=-10

x=-2 and y=-2

Answer:

B