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After you're done solving a system, you'll be able to check your answers.

Check it out:

By magic, we know that01-systems-12a.gif is the solution to the system

 

    x - y + z = 7

2x + 3y - z = -8

 4x + y - 2z = -6

Let's check that!

x - y + z = 7 ... 1 - ( -2 ) + 4 = 7 ... 7 = 7 ...yep!2x + 3y - z = -8 ... 2 ( 1 ) + 3 ( -2 ) - 4 = -8 ... -8 = -8 ... yep!

4x + y - 2z = -6 ... 4 ( 1 ) + ( -2 ) - 2 ( 4 ) = -6 ... -6 = -6 ... yep!

It's REALLY important to check all three equations.  It's possible to make a mistake and have your answers work in one or two of them!


TRY IT:

Verify that (5, -1, 2) is the solution to

     5x - 2y + z = 29

-3x + 4y - 2z = -23

        x + 6y - 7z = -15