SAT Question fb5e7f59: Systems of Linear Equations answer and explanation with Desmos solution

It's given that the graphs of the equations in the given system intersect at the point $(q,19)$, where $q$ is a constant. Therefore, the coordinates of this point must satisfy both equations. Substituting the point $(q,19)$ into the first equation, $-x-wy=-337$, yields $-q-w(19)=-337$. Adding $19w$ to both sides of this equation yields $-q=-337+19w$, which is equivalent to $q=337-19w$. Substituting the point $(q,19)$ into the second equation yields $2q-w(19)=47$. Substituting $337-19w$ in place of $q$ in the equation $2q-w(19)=47$ yields $2(337-19w)-19w=47$. Applying the distributive property to the left-hand side of this equation yields $674-38w-19w=47$. Combining like terms on the left-hand side of this equation yields $674-57w=47$. Subtracting $674$ from both sides of this equation yields $-57w=-627$. Dividing both sides of this equation by $-57$ yields $w=11$.