systems in 3 variables

Question

Mei and Ted are selling cheesecakes for a school fundraiser. Customers can buy pecan cheesecakes and chocolate marble cheesecakes. Mei sold 6 pecan cheesecakes and 12 chocolate marble cheesecakes for a total of $168. Ted sold 12 pecan cheesecakes and 8 chocolate marble cheesecakes for a total of $160. What is the cost each of one pecan cheesecake and one chocolate marble

cheesecake?

Answer 1

X= pecan cheesecake

y= marble cheesecake

6x+12y=168 (eq1)

12x+12y=160 (eq.2)

Multiply eq 1 by 12 and eq.2 by 6 then we get

72x+144y=2016

72x+48y= 960 change the sign and subtract we get

96y= 1056

y=11

plug y value in eq 1

6x+12(11)= 168

6x+132= 168

6x=36

x=6