SAT Question dcc4886a: Systems of Linear Equations answer and explanation with Desmos solution

Choice D is correct. It's given that the system has infinitely many solutions. The graphs of two lines in the xy-plane represented by equations in slope-intercept form, $y=mx+b$, where $m$ and $b$ are constants, have infinitely many solutions if their slopes, $m$, are the same and if their y-coordinates of the y-intercepts, $b$, are also the same. The first equation in the given system is $y=\frac{2}{7}x+3$. For this equation, the slope is $\frac{2}{7}$ and the y-coordinate of the y-intercept is $3$. If the second equation is in the form $y=mx+b$, then for the two equations to be equivalent, the values of $m$ and $b$ in the second equation must equal the corresponding values in the first equation. Therefore, the second equation must have a slope, $m$, of $\frac{2}{7}$, and a y-coordinate of the y-intercept, $b$, of $3$. Thus, the value of $b$ is $3$.