SAT Question a0489274: Systems of Linear Equations answer and explanation with Desmos solution

Choice B is correct. It's given by the first equation in the system that $y=-\frac{1}{5}x$. Substituting $-\frac{1}{5}x$ for $y$ in the second equation in the system, $y=\frac{1}{7}x$, yields $-\frac{1}{5}x=\frac{1}{7}x$. Adding $-\frac{1}{5}x$ to both sides of this equation yields $0=\frac{1}{7}x+\frac{1}{5}x$, which is equivalent to $0=\frac{5}{35}x+\frac{7}{35}x$, or $0=\frac{12}{35}x$. Multiplying both sides of this equation by $\frac{35}{12}$ yields $0=x$. Therefore, the value of $x$ is $0$.