SAT Question 79be5180: Systems of Linear Equations answer and explanation with Desmos solution

It's given that $y=9x+12$. Substituting $9x+12$ for $y$ in the second equation in the system, $x+7y=20$, yields $x+7\left(9x+12\right)=20$, which gives $x+63x+84=20$, or $64x+84=20$. Subtracting $84$ from each side of this equation yields $64x=-64$. Dividing each side of this equation by $64$ yields $x=-1$. Substituting $-1$ for $x$ in the first equation in the system, $y=9x+12$, yields $y=9\left(-1\right)+12$, or $y=3$. Therefore, the value of $y$ is $3$.