Question

Please do elimination method 2x-9y=-36
-14x+18y=-18

Answer 1

The solution to the system of equations will be:

`x=9,\:y=6`

Explanation:

Given the system of equations

`\begin{bmatrix}2x-9y=-36\\ -14x+18y=-18\end{bmatrix}`

Multiply 2x-9y=-36 by 7

`14x-63y=-252`

so the system of equations becomes

`\begin{bmatrix}14x-63y=-252\\ -14x+18y=-18\end{bmatrix}`

Adding both equations

`-14x+18y=-18`

`+`

`\underline{14x-63y=-252}`

`-45y=-270`

solve -45y = -270 for y

`-45y=-270`

divide both sides by -45

`(-45y)/(-45)=(-270)/(-45)`

Simplify

`y=6`

For 14x-63y = -270 plug in y = 6

`14x-63\cdot \:6=-252`

`14x-378=-252`

Add 378 to both sides

`14x-378+378=-252+378`

Simplify

`14x=126`

Divide both sides by 14

`(14x)/(14)=(126)/(14)`

Simplify

`x=9`

Therefore, the solution to the system of equations will be:

`x=9,\:y=6`