Question

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?

Answer 1

2*CD + 3*DVD = 31

Answer 2

CD + DVD = 12

Answer 3

Solve for CDs and DVDs

Answer 4

Answers are:
10
7
5
2

Answer 5

So...

2CD + 3DVD = 31
-2(CD + DVD = 12)
-2CD + (-2DVD) = -24
DVD = 7

?

Answer 6

why are you multiplying by -2?

Answer 7

You have two equations:

x = CDs, y =DVDs.

1. 2x +3y = 31

2. x + y = 12

Take the second equation, x + y = 12, solve for 1, either x (CDs) or y (DVDs), and plug it into your first equation and solve for the first variable, then use that number to solve for the second variable.

Answer 8

@jhannybean he confused you a bit with the notation — he multiplied the second equation by -2, thus eliminating the CD variable when they were combined.

if done with your notation,

\[2x+3y=31\]\[x+y=12\]multiply second eq. by -2 and combine
\[2x+3y=31\]\[-2x-2y=-24\]----------------
\[y=7\]

Answer 9

substitution is easy, but elimination can be even easier :-)

Answer 10

Truee...