Substitution

Question

3x+2y-z=1

2x+y-z=-2

2x-y-2z=4

Answer 1

Tell you what, Joe: I'm gonna walk through this one step-by-step. Then you follow the same steps and solve the other one you posted yourself, OK? :-)

First of the three equations:

3x + 2y - z = 1
Solve that for z and get

 

z = 3x + 2y - 1

Second of the three equations:

2x + y - z = -2

Stick your definition for z in there and get

 

2x + y - (3x + 2y - 1) = -2  OR

-x - y = -3

Third of the three equations:

2x - y - 2z = 4

Stick your definition for z in there also, and get

 

2x - y - 2(3x + 2y - 1) = 4  OR

-4x - 5y = 2

 

We're still doing substitution. But now we have

-x - y = -3  OR

y = -x + 3

We also have

-4x - 5y = 2

and we can substitute y = -x +3 in there!

 

-4x - 5(-x + 3) = 2 OR

x = 17 and you're done. Work your way back to get y and z.

 

Sanity check: usually (not always) a tough system of equations like this is accompanied by an answer in nice whole numbers, when it's a problem in your textbook. Makes the calculations easier. Me, I used Wolfram Alpha to check my hand-calculation here and got the same value for x. You might consider doing the same. Cheers!