Question

Find the solution to the system of equations below. 2y = 2x - 8 2x + y = 5

Answer 1

Answer:

The solution to the system of equations is:

• (x, y) = (3, -1)

The graph is attached below.

Step-by-step explanation:

Given the system of equations

$2y = 2x - 8$

$2x + y = 5$

Let us solve the system of equations using the elimination method

$\begin{bmatrix}2y=2x-8\\ 2x+y=5\end{bmatrix}$

Arrange equation variables for elimination

$\begin{bmatrix}2y-2x=-8\\ y+2x=5\end{bmatrix}$

Multiply y + 2x = 5 by 2:  2y + 4x = 10

$\begin{bmatrix}2y-2x=-8\\ 2y+4x=10\end{bmatrix}$

subtracting the equations

$2y+4x=10$

$-$

$\underline{2y-2x=-8}$

$6x=18$

solve 6x = 18 for x

$6x=18$

Divide both sides by 6

$\frac{6x}{6}=\frac{18}{6}$

simplify

$x=3$

For 2y - 2x = -8  plug in x = 3

$2y-2\cdot \:3=-8$

$2y-6=-8$

Add 6 to both sides

$2y-6+6=-8+6$

Simplify

$2y=-2$

Divide both sides by 2

$\frac{2y}{2}=\frac{-2}{2}$

Simplify

$y=-1$

Therefore, the solution to the system of equations is:

• (x, y) = (3, -1)

The graph is attached below.