Question

I need help
Y=3-2x
-4x-4y=-20

Answer 1

The solution to the system of equations

`x=-2` ,
`y=7`

Explanation:

Given the system of equations

`\begin{bmatrix}y=3-2x\\ -4x-4y=-20\end{bmatrix}`

`\mathrm{Arrange\:equation\:variables\:for\:elimination}`

`\begin{bmatrix}y+2x=3\\ -4y-4x=-20\end{bmatrix}`

`\mathrm{Multiply\:}y+2x=3\mathrm{\:by\:}4\:\mathrm{:}\:\quad \:4y+8x=12`

`\begin{bmatrix}4y+8x=12\\ -4y-4x=-20\end{bmatrix}`

`-4y-4x=-20`

`+`

`\underline{4y+8x=12}`

`4x=-8`

so

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

solving for x

`4x=-8`

Divide both sides by 4

`(4x)/(4)=(-8)/(4)`

`(4x)/(4)=(-8)/(4)`

`x=-2`

`\mathrm{For\:}4y+8x=12\mathrm{\:plug\:in\:}x=-2`

`4y+8\left(-2\right)=12`

`4y-16=12`

`4y=28`

Divide both sides by 4

`(4y)/(4)=(28)/(4)`

`y=7`

Thus, the solution to the system of equations

`x=-2` ,
`y=7`