How do you solve for z?

Question

x + y + z = 5
2x - 3z = 7
3x - y + z = 1

Answer 1

You need to get z all by itself.

x + y + z = 5

Subtract x from both sides. y + z = 5 - x

Subtract y from both sides. z = 5 - x - y

It works just the same if there is a coefficient. So in the 2nd problem you would subtract 2x from both sides and then divide by negative 3 so the answer would look like:

2x - 3z = 7

-3z = 7 - 2x

z = (7 - 2x)/-3

Just do the third one the same way.

Answer 2

x + y + z = 5
2x - 3z = 7
3x - y + z = 1(-1)

x + y + z = 5
-3x + y - z = -1
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-2x + 2y = 4
2y=4+2x
y=2+x

2x - 3z = 7
-3z=7-2x
z=(2x-7)/3

x + y + z = 5
x + 2+x + 2x/3 -7/3 = 5
2x + 2/3x = 5 -2 + 7/3
6+2/3 x = 9+7/3
8/3x = 16/3
x=16/3 * 3/8
x=2

z= (2x-7)/3
z=2(2)-7/3
z=-3/3
z= -1

Answer 3

Delete y using two different "given" equations.
Then eliminate x. Once you eliminate x you can find z.

x + y + z = 5
3x - y + z = 1 ADD together, which deletes the y.
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4x + 2z = 6

2x - 3z = 7 Multiply both sides of this "given" equation by -2 to rid of x's when you add it to the latest equation you just found.
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-4x + 6z = -14
4x + 2z = 6 ADD the new equation you found above.
----------------------------------
8z = -8 Divide each side by 8

z = -1 ANSWER


PS If you would like to see how to solve for x & y as well...
Take your "z" you found and plug it into one of the equations:

2x - 3z = 7
2x - 3(-1) = 7
2x = 4
x = 2

Then, take your "z" & "x" and plug into any equation to find y:

x + y + z = 5
2 + y -1 = 5
y = 4

If you would like an answer check for x, y & z:
x + y + z = 5
2 + 4 -1 = 5 check.

2x - 3z = 7
2(2) - 3(-1) = 7 check.

3x - y + z = 1
3(2) - 4 -1 = 1 check.

:) Hope that helps.