Answer:
The solution to the system of equations is:
The graph is attached below.
Step-by-step explanation:
Given the system of equations
[tex]2y = 2x - 8[/tex]
[tex]2x + y = 5[/tex]
Let us solve the system of equations using the elimination method
[tex]\begin{bmatrix}2y=2x-8\\ 2x+y=5\end{bmatrix}[/tex]
Arrange equation variables for elimination
[tex]\begin{bmatrix}2y-2x=-8\\ y+2x=5\end{bmatrix}[/tex]
Multiply y + 2x = 5 by 2: 2y + 4x = 10
[tex]\begin{bmatrix}2y-2x=-8\\ 2y+4x=10\end{bmatrix}[/tex]
subtracting the equations
[tex]2y+4x=10[/tex]
[tex]-[/tex]
[tex]\underline{2y-2x=-8}[/tex]
[tex]6x=18[/tex]
solve 6x = 18 for x
[tex]6x=18[/tex]
Divide both sides by 6
[tex]\frac{6x}{6}=\frac{18}{6}[/tex]
simplify
[tex]x=3[/tex]
For 2y - 2x = -8 plug in x = 3
[tex]2y-2\cdot \:3=-8[/tex]
[tex]2y-6=-8[/tex]
Add 6 to both sides
[tex]2y-6+6=-8+6[/tex]
Simplify
[tex]2y=-2[/tex]
Divide both sides by 2
[tex]\frac{2y}{2}=\frac{-2}{2}[/tex]
Simplify
[tex]y=-1[/tex]
Therefore, the solution to the system of equations is:
The graph is attached below.
