Phillip bought 12 used cds and dvds. cds cost $2 each, and dvds cost $3 each. he spent $31, not including tax. how many dvds did phillip buy?

So he bought 12 CDs and DVDs (in total), CDs + DVDs = 12

Each cd is 2 and each cd is 3

Total spent = 31 (2*x + 3*y)

I call x cds and y dvds

x+y = 12

2x+3y = 31

Solve for y

Move x to the right with changed sign

y = 12-x (DVDs, you can also write x = 12-y)

And substitute 12-y in the equation

2x + 3(12-x) = 31

2x + 36 - 3x = 31

2x - 3x = 31 - 36

-x = -5

x = 5 (CDs)

To find DVDs let's rewrite y = 12-x

y = 12-5 = 7 (DVDs)