Question

X + 2y = 11
Y = x - 2

Answer 1

The solution to the system of equations is:

`x=5,\:y=3`

Explanation:

Given the system of equations

`\begin{bmatrix}x+2y=11\\ y=x-2\end{bmatrix}`

Arrange equation variables for elimination

`\begin{bmatrix}x+2y=11\\ -x+y=-2\end{bmatrix}`

adding

`-x+y=-2`

`+`

`\underline{x+2y=11}`

`3y=9`

so

`\begin{bmatrix}x+2y=11\\ 3y=9\end{bmatrix}`

solving for y

`3y=9`

Divide both sides by 3

`(3y)/(3)=(9)/(3)`

`y=3`

`\mathrm{For\:}x+2y=11\mathrm{\:plug\:in\:}y=3`

`x+2\cdot \:3=11`

`x+6=11`

`x=5`

Thus, the solution to the system of equations is:

`x=5,\:y=3`