SAT Question 4edecdba: Linear Equations In Two Variables answer and explanation with Desmos solution

It’s given that the equation $8x+11y=170$ gives the possible combinations of the number of $2009$ premium grade Log Cabin Pennies, $x$, and the number of $1996$ select grade Lincoln Pennies, $y$, in a collection that is worth a total of $$170$. It’s also given that there are $6$

$1996$ select grade Lincoln Pennies in the collection, and thus $y=6$. Substituting $6$ for $y$ in the given equation yields $8x+11(6)=170$, or $8x+66=170$. Subtracting $66$ from both sides of this equation yields $8x=104$. Dividing both sides of this equation by $8$ yields $x=13$. Therefore, there are $13$

$2009$ premium grade Log Cabin Pennies in the collection.