Question

PLEASE HELP!!!!!!!!!!!!!!!!!!

Answer 1

The solution to the system of equations be:

`y=-3,\:x=2`

Explanation:

Given the system of equations

`\begin{bmatrix}y=3x-9\\ y=-2x+1\end{bmatrix}`

Let us solve the system by the elimination method

`\begin{bmatrix}y=3x-9\\ y=-2x+1\end{bmatrix}`

Arrange equation variables for elimination

`\begin{bmatrix}y-3x=-9\\ y+2x=1\end{bmatrix}`

subtracting the equations

`y+2x=1`

`-`

`\underline{y-3x=-9}`

`5x=10`

so the system of equations becomes

`\begin{bmatrix}y-3x=-9\\ 5x=10\end{bmatrix}`

solve 5x for x

`5x=10`

Divide both sides by 5

`(5x)/(5)=(10)/(5)`

`x = 2`

`\mathrm{For\:}y-3x=-9\mathrm{\:plug\:in\:}x=2`

`y-3\cdot \:2=-9`

`y-6=-9`

Add 6 to both sides

`y-6+6=-9+6`

`y=-3`

Therefore, the solution to the system of equations be:

`y=-3,\:x=2`