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?