Answer:
D. [tex]x=-5,y=\frac{5}{4}[/tex]
Step-by-step explanation:
[tex]\begin{bmatrix}5x+4y=-20\\ 5x+12y=-10\end{bmatrix}[/tex]
Subtract Equation 2 - Equation 1:
[tex]5x+12y=-10\\-\\\underline{5x+4y=-20}\\8y=10[/tex]
Divide both sides by 8:
[tex]\frac{8y}{8}=\frac{10}{8}[/tex]
[tex]y=\frac{5}{4}[/tex]
Substitute [tex]y=\frac{5}{4}[/tex] into Equation 1:
[tex]5x+4y=-20[/tex]
[tex]5x+4\times \frac{5}{4}=-20[/tex]
[tex]5x+5=-20[/tex]
Subtract 5 from both sides:
[tex]5x+5-5=-20-5[/tex]
[tex]5x=-25[/tex]
Divide both sides by 5:
[tex]\frac{5x}{5}=\frac{-25}{5}[/tex]
[tex]x=-5[/tex]
