Answer:
The solution to the system of equations
[tex]x=-2[/tex] , [tex]y=7[/tex]
Step-by-step explanation:
Given the system of equations
[tex]\begin{bmatrix}y=3-2x\\ -4x-4y=-20\end{bmatrix}[/tex]
[tex]\mathrm{Arrange\:equation\:variables\:for\:elimination}[/tex]
[tex]\begin{bmatrix}y+2x=3\\ -4y-4x=-20\end{bmatrix}[/tex]
[tex]\mathrm{Multiply\:}y+2x=3\mathrm{\:by\:}4\:\mathrm{:}\:\quad \:4y+8x=12[/tex]
[tex]\begin{bmatrix}4y+8x=12\\ -4y-4x=-20\end{bmatrix}[/tex]
[tex]-4y-4x=-20[/tex]
[tex]+[/tex]
[tex]\underline{4y+8x=12}[/tex]
[tex]4x=-8[/tex]
so
[tex]\begin{bmatrix}4y+8x=12\\ 4x=-8\end{bmatrix}[/tex]
solving for x
[tex]4x=-8[/tex]
Divide both sides by 4
[tex]\frac{4x}{4}=\frac{-8}{4}[/tex]
[tex]\frac{4x}{4}=\frac{-8}{4}[/tex]
[tex]x=-2[/tex]
[tex]\mathrm{For\:}4y+8x=12\mathrm{\:plug\:in\:}x=-2[/tex]
[tex]4y+8\left(-2\right)=12[/tex]
[tex]4y-16=12[/tex]
[tex]4y=28[/tex]
Divide both sides by 4
[tex]\frac{4y}{4}=\frac{28}{4}[/tex]
[tex]y=7[/tex]
Thus, the solution to the system of equations
[tex]x=-2[/tex] , [tex]y=7[/tex]
