Acorner store sells two kinds of baked goods: cakes and pies. a cake costs 5$ and a pie costs 7$. in one day, the store sold 15 baked goods for a total of 91$. how many cakes did they sell?

Set up a system of equations:




x is how many cakes were made, y is how many pies were made, 5 represents the cost of each cake, and 7 represents the cost of each pie.

We'll solve the system through elimination. Multiply the entire first equation by -5:



The system should now look like this:




Combine the two equations to eliminate x:



Divide both sides by 2 to get y by itself:



There were 8 pies made.

Plug in the value for y into the original first equation:



Subtract both sides by 8 to get x by itself:



There were 7 cakes made.