Question

What is the x value of the solution to the system shown?
2y = 2x + 12
2-y=4

Answer 1

`x = -8`

Explanation:

`\begin{cases}2y = 2x + 12\\2-y = 4\end{cases}`

It would be easier to start with the second equation.

`2 - y = 4 \text{ // Add y and subtract 4}\\\to 2 - y - 4 = 4 - y - 4\\\to -2 = y`

From here, we can substitute
`y = -2` into the first equation, to solve for
`x`.

`2(-2) = 2x + 12\\\to -4 = 2x + 12 \text{ // Subtract 12 on both sides}\\\to -4 - 12 = 2x + 12 - 12\\\to -16 = 2x \text{ // Divide by 2}\\\to -\frac{16}2 = \frac{2x}2\\\to -8 = x`