Originally Posted by

**LisaH** Hi,

Im trying to work out a math problem I have tonight. I have the general idea of what I should be doing but it just isnt panning out for me. I need to solve for x,y and z. I keep redoing this problem and keep getting different answers. Could someone help me out?

The equations

x-y+2z=7

2x+3y-z=-6

-x+2y+z=-3

This is what I did so far:

-2(x-y+2z=7) ==> -2x+2y-4z=-14

==2nd equation====> 2x+3y-z=-6

_____________

5y-5z=-20

2(-x+2y+z=-3) ==> -2x+4y+2z=-6

===2nd equat.====> 2x+3y-z=-6

____________

7y+z=-12

Then I took the simplified equations and solved for the y variable using the addition method

5(7y+z=-12) ====> 35y+5z=60 **should be -60**

===2nd equation==> 5y-5z=-20

_________

40y=40 **should be -80**

y=1 **should be -2**

**You have found "y"**

**Therefore, substituting into 5y-5z=-20 or y-z=-4 gives -2-z=-4 so z=2**

**Then x-y+2z=7 gives x+2+4=7 so x=1**

**THERE WAS NO NEED TO MAKE THE REMAINING CALCULATIONS BELOW**

UNLESS YOU JUST WANT TO PRACTICE.

ONCE YOU HAVE FOUND ONE VALUE, YOU ONLY NEED SUBSTITUTE IT BACK TO GET THE OTHERS.

(2x+3y-z=-6)2====> 4x+6y-2z=-12

===2nd equation===> x-y+2z=7

-------------------

5x+5y=-5

2x+3y-z=-6

-x+2y+z=-3

------------

x+5y=-9

Solve for x

-1(x+5y=-9)==>-x-5y=9

============>5x+5y=-5

----------------

4x=4

x=1

plug both x and y into one of the original 3 equations to solve for z

x-y+2z=7 ===> 1-1+2z=7

===========> 2z=7

===========z=7/2

check with another equation

2x+3y-z=-6 ===> 2(1)+3(1)-(7/2)=-6

=============> 5-(7/2)=-6

===============3/2=6 which is Wrong!!

Can someone help me see where I am going wrong?