The first equation represents Beth selling cheesecakes and the second equation represent Aliyah selling cheesecakes.
7F + 10C = 316 (1)
5F + 5C = 185 (2)
Let F be the price of a French cheesecake and let C be the price of a chocolate cheesecake.
We need to solve the system of linear equations by elimination method. Multiply (2) by -2 to eliminate the variable C.
7F + 10C = 316 (1)
-10F - 10C = -370 (3)
Add the two equations above and we will get: -3F = -54
Divide both sides by -3 to get: F = 18
Plug in F = 18 to one of the two original equations to find C. Let's choose the second equation so we can deal with smaller numbers.
5(18) + 5C = 185 ⇒ 90 + 5C = 185 ⇒ 5C = 95 ⇒ C = 19
Now that we found the values of C and F, lets check our solutions.
7(18) + 10(19) = 126 + 190 = 316
5(18) + 5(19) = 90 + 95 = 185
The cost of one French cheesecake is $18 and the cost of one chocolate cheesecake is $19.
