SAT Question 1b1deebe: Systems of Linear Equations answer and explanation with Desmos solution

Choice D is correct. It's given that the graphs of the given system of equations intersect at the point $\left(4,y\right)$. Therefore, $\left(4,y\right)$ is the solution to the given system. Multiplying the first equation in the given system by $-2$ yields $-2ax-2by=-144$. Adding this equation to the second equation in the system yields $\left(-2a+6\right)x+\left(-2b+2b\right)y=\left(-144+56\right)$, or $\left(-2a+6\right)x=-88$. Since $\left(4,y\right)$ is the solution to the system, the value of $a$ can be found by substituting $4$ for $x$ in this equation, which yields $\left(-2a+6\right)\left(4\right)=-88$. Dividing both sides of this equation by $4$ yields $-2a+6=-22$. Subtracting $6$ from both sides of this equation yields $-2a=-28$. Dividing both sides of this equation by $-2$ yields $a=14$.