Question

Which is the correct answer when solving the equation using

elimination?

1. -4x - 2y = -12
4x + 8y = -24

A. (6,-6) because I was able to eliminate my y terms first
B.(-6,6) because I was able to eliminate my y terms first
C.(6,-6) because I was able to eliminate my x terms first
D.(-6.6) because I was able to eliminate my x terms first

Answer 1

We conclude that the correct option is 'A'.

As I was able to get (6, -6) because I was able to eliminate my y terms first.

Explanation:

Given the system of equations

`\begin{bmatrix}-4x-2y=-12\\ 4x+8y=-24\end{bmatrix}`

solving using the elimination method

`4x+8y=-24`

`+`

`\underline{-4x-2y=-12}`

`6y=-36`

so

`\begin{bmatrix}-4x-2y=-12\\ 6y=-36\end{bmatrix}`

solve for y

`6y=-36`

Divide both sides by 6

`(6y)/(6)=(-36)/(6)`

`y=-6`

`\mathrm{For\:}-4x-2y=-12\mathrm{\:plug\:in\:}y=-6`

`-4x-2\left(-6\right)=-12`

`-4x+12=-12`

`-4x=-24`

Divide both sides by -4

`(-4x)/(-4)=(-24)/(-4)`

`x=6`

Thus, the solutions are:

`x=6,\:y=-6`

Therefore, we conclude that the correct option is 'A'.

As I was able to get (6, -6) because I was able to eliminate my y terms first.