Question

Y=-3x-5
y=4x+30
solve and I need to show my work to

Answer 1

The solution to the system of equation

`y=10,\:x=-5`

Explanation:

Given the system of equation

`\begin{bmatrix}y+3x=-5\\ y-4x=30\end{bmatrix}`

Arrange equation variables for elimination

`\begin{bmatrix}y+3x=-5\\ y-4x=30\end{bmatrix}`

subtracting the equation

`y-4x=30`

`-`

`\underline{y+3x=-5}`

`-7x=35`

`\begin{bmatrix}y+3x=-5\\ -7x=35\end{bmatrix}`

solve -7x = 35 for x

`-7x=35`

divide both sides by -7

`(-7x)/(-7)=(35)/(-7)`

`x=-5`

For y + 3x = -5 plug in x = -5

`y+3\left(-5\right)=-5`

`y-15=-5`

Add 15 to both sides

`y-15+15=-5+15`

Simplify

`y=10`

Therefore, the solution to the system of equation

`y=10,\:x=-5`