Expert: Paul Klarreich - 4/18/2007

Question
i need help solving this equation for 3 variables. i need to figure out what x y and z equal.

3x+2y-7z=21
x-2y+3z=15
2x-y+2=7

Answer
Questioner:   larissa
Category:  Advanced Math
 
Subject:  Algebra 2
Question:  i need help solving this equation for 3 variables. i need to figure out what x y and z equal.

3x+2y-7z=21
x-2y+3z=15
2x-y+2=7
................................................
Hi, Larissa,

These require little more than a little inspection to find the simplest approach, a little insight as to the type of work involved, and A GOOD AMOUNT OF SWEAT to work them out.

3x + 2y - 7z = 21  [A]
x - 2y + 3z = 15  [B]
2x -  y + 2z =  7  [C] << is that what you meant?

When you handled equations in TWO variables, you used eliminaton to reduce to one equation in one variable.  So here, you use elimination to reduce to two equations in two variables.  Then you will know what to do.


I am not going to work out the whole thing BECAUSE I think you mistyped something.  You can decide.

Let's eliminate 'y' from the two equations.  We have +2y and -2y in A and B, so that makes it nice.

4x        - 4z = 36   [A + B]
x        -  z =  9   [A + B, divided by 4]

We have +2y and - y  in A and C, so A+2C should eliminate y.  [We eliminate the same variable both times, otherwise we don't make progress.]

3x + 2y - 7z = 21  [A]
4x - 2y + 4z =  7  [2C]
-------------------------
7x      - 3z = 28  [A + 2C]

Now you have two equations in two variables:

x        -  z =  9
7x        - 3z = 28

Solve these equations for x and z.  When you are done, take those values and substitute into ANY ONE of the A,B,C to find the value of y.

Then check the whole thing in equations A,B,C.