SOLUTION: Hi, I have a problem that deals with linear equations with three variables: SOLVE: x+y=7 y+z=8 x+2z=2 and no, I cannot simply use matrices to solve this question. I tried el

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Question 989590: Hi, I have a problem that deals with linear equations with three variables:
SOLVE:
x+y=7
y+z=8
x+2z=2
and no, I cannot simply use matrices to solve this question. I tried eliminating 'z' from the second and third equation, but I got stuck because I can't eliminate 'z' from the first equation. Please help and thank you so much to whoever helps!
Found 2 solutions by stanbon, MathTherapy:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
SOLVE:
x+y=7
y+z=8
x+2z=2
----
express y and x in terms of "z"::
y = 8-z
x = 2-2z
------
Substitute for x and y and solve for "z"::
2-2z + 8-z = 7
-3z + 10 = 7
-3z = -3
z = 1
----
y = 8-z = 7
x = 2 - 2z = 2-2 = 0
----------
Cheers,
Stan H.
-------------
Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!

Hi, I have a problem that deals with linear equations with three variables:
SOLVE:
x+y=7
y+z=8
x+2z=2
and no, I cannot simply use matrices to solve this question. I tried eliminating 'z' from the second and third equation, but I got stuck because I can't eliminate 'z' from the first equation. Please help and thank you so much to whoever helps!
 x + y = 7_____y = 7 - x ------- eq (i)

    y + z = 8 ------ eq (ii)

   x + 2z = 2 ------ eq (iii)

7 - x + z = 8 ------ Substituting 7 - x for y in eq (ii)

  - x + z = 1 ------ eq (iv)

       3z = 3 ------ Adding eqs (iv) and (iii)

        z = , or 

Complete this by substituting 1 for z in eq (ii) to determine the value of y, and finally, substitute the value of y into eq (i) to get the value of x 

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