SAT Question 571174f3: Systems of Linear Equations answer and explanation with Desmos solution

It's given that the system has infinitely many solutions. A system of two linear equations has infinitely many solutions if and only if the two linear equations are equivalent. Multiplying each side of the first equation in the system by $\frac{35}{4}$ yields $\frac{35}{4}\left(\frac{2}{5}x+\frac{7}{5}y\right)=\frac{35}{4}\left(\frac{2}{7}\right)$, or $\frac{7}{2}x+\frac{49}{4}y=\frac{5}{2}$. Since this equation is equivalent to the second equation and has the same right side as the second equation, the coefficients of $x$ and $y$, respectively, should also be the same. It follows that $g=\frac{7}{2}$ and $k=\frac{49}{4}$. Therefore, the value of $\frac{g}{k}$ is $\frac{\frac{7}{2}}{\frac{49}{4}}$, or $\frac{2}{7}$. Note that 2/7, .2857, 0.285, and 0.286 are examples of ways to enter a correct answer.