# Solve the following systems of linear equations, showing all work: 2x+y-z = 14 x+2y-z = 12 2x-2y+z = 3

2x+y-z = 14

x+2y-z = 12

2x-2y+z = 3

Both of the previous answers are helpful but they are also different answers.  You have to decide which value of z is correct.

The best way to check your answers is to plug in the values and see which one works...

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2x+y-z = 14

x+2y-z = 12

2x-2y+z = 3

Both of the previous answers are helpful but they are also different answers.  You have to decide which value of z is correct.

The best way to check your answers is to plug in the values and see which one works for ALL THREE EQUATIONS, not just one!

When I use 5, 3, and 1 I get...

2(5) + 3 - 1 = 14

10 + 3 - 1 = 14

12 does not equal 14

These values don't work for the equations.

On the other hand, when I try 5, 3, and -1, I get the following:

2(5) + 3 - (-1) = 14

10 + 3 + 1 = 14

14 = 14

5 + 2(3) -(-1) = 12

5 + 6 + 1 = 12

12 = 12

2(5) - 2(3) + (-1) = 3

10 - 6 - 1 = 3

3 = 3

Obviously, these are the correct answers.

Approved by eNotes Editorial Team