SAT Question b00ad7f2: Systems of Linear Equations answer and explanation with Desmos solution

Choice C is correct. Adding $9x$ to both sides of the first equation in the given system yields $y=9x+13$. Substituting the expression $9x+13$ for $y$ in the second equation in the given system yields $5x=2\left(9x+13\right)$. Distributing the $2$ on the right-hand side of this equation yields $5x=18x+26$. Subtracting $18x$ from both sides of this equation yields $-13x=26$. Dividing both sides of this equation by $-13$ yields $x=-2$. Substituting $-2$ for $x$ in the equation $y=9x+13$ yields $y=9\left(-2\right)+13$, or $y=-5$. Therefore, the solution $\left(x,y\right)$ to the given system of equations is $\left(-2,-5\right)$.