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Most of the time they aren't set up that nicely.  You'll usually have to do a little dinking before something will drop out.

Look at this one:

3x - 4y = -5 and 5x - 2y = -6

If we just add straight down, nothing's going to drop out and we'll just get a mess.

But, check out the y guys:

3x - 4y = -5 and 5x - 2y = -6
If we could make this a +4y,
the
y's would drop out...

So, let's do it!  Remember that we can multiply an equation by a number...  So, let's multiply the second equation by a -2:

3x - 4y = -5 and -2 ( 5x - 2y = -6 )

Remember to hit each guy!

( 3x - 4y = -5 ) + ( -10x + 4y = 12 ) = ( -7x + 0 = 7 ) ... -7x = 7 ... x = -1

Now, stick the x guy into either of the original equations.  I'm going to go for the first one:

stick the x = -1 into 3x - 4y = -5 for x, which gives 3 ( -1 ) - 4y = -5 ... -3 - 4y = -5 ... -4y = -2 ... y = 1 / 2

 

The answer is (-1, 1 / 2)

Check it - and don't let that fraction freak you...  These things happen!


YOUR TURN:

Solve by elimination:

2x + 5y = 5 and -6x + 7y = -37

* Hint: ditch the x!