Question

solve each system using elimination
3p + q = 7
2p - 2q = -6

Answer 1

To solve by elimination, you multiply an entire equation by LCM to cancel out a variable.
In other words, if you want to cancel q, multiply the top equation by 2. Or you could cancel p by multiplying -2 on the top, and positive 3 on the bottom... get it?

*2 3p + q = 7 6p + 2q = 14
2p - 2q = -6 2p - 2q = -6

Then you add them together:

6p + 2q = 14
2p - 2q = -6
8p = 8
/8 /8
p = 1

Now you can substitute o into an original equation to find q

3(1) + q = 7
3 + q = 7
-3 -3
q = 4
Then check in both equations:

3(1) + (4) = 7 (check!)
2(1) - 2(4) = -6 (check!)