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Sometimes, you'll have to make adjustments to both equations to get something to drop out.  When possible, always go after the easier numbers!

Let's do this one:

                           2x - 9y = 8 and -5x + 8y = -20 ... the 2 and -5 are easier than the -9 and 8
We want to make these 10x and -10x:

5 ( 2x - 9y = 8 ) and 2 ( -5x + 8y = -20 )

Remember to hit each guy!

* It's easy to forget the last guys.

( 10x - 45y = 40 ) + ( -10x + 16y = -40 ) = -29y = 0 ... y = 0

Let's stick y = 0 into the first equation:

stick y = 0 into 2x - 9y = 8 for y, which gives 2x - 9 ( 0 ) = 8 ... 2x = 8 ... x = 4

The answer is (4, 0).

Check it!


YOUR TURN:

Solve by elimination:

13x - 2y = 25 and 4x + 3y = -14

* Use your head...  Which numbers are easier?