x - y + z = 4
2x + y - 3z = -5
x + 3y + 2z = 2
Choose a letter to eliminate, and
choose two of the equations that contain
that letter to eliminate it from.
I choose to eliminate y from the first two
equations since all I have to do is add
the equations as they are and the y's
will cancel out
x - y + z = 4
2x + y - 3z = -5
-----------------
3x - 2z = -1
Choose the equation you haven't chosen yet,
and another one that you have already used,
to eliminate the SAME letter you eliminated
before.
I haven't used the 3rd one, so I will choose
it and the first one to eliminate the SAME
letter I eliminated before, which is y:
x - y + z = 4
x + 3y + 2z = 2
To eliminate y we must first multiply the
first equation by 3:
3x - 3y + 3z = 12
x + 3y + 2z = 2
-----------------
4x + 5z = 14
So we take the two equations with y eliminated
and solve them:
3x - 2z = -1
4x + 5z = 14
Now we eliminate z by multiplying the first by 5
and the second by 2
15x - 10z = -5
8x + 10z = 28
---------------
23x = 23
23x = 23
x = 1
Substitute 1 for x in
3x - 2z = -1
3(1) - 2z = -1
3 - 2z = -1
-2z = -4
z = 2
Substitute x = 1 and z = 2 into
one of the original equations,
say the first:
x - y + z = 4
1 - y + 2 = 4
-y + 3 = 4
-y = 1
y = -1
Solution: (x, y, z) = (1, -1, 2)
Edwin
