Question

Use the substitution method to solve the following system of equations.

x + 2y - z = 7
4x - y + 3z = -2
2x + 2y - z = 9

Can somebody please show me how todo this? I've gotten to this:
Z = 20

But then I try to solve for Y and come out to it equaling 15.1 repeating, which I know can't be right. Anybody know where I'm probably going wrong? :/

Answer 1

You should use the top and bottom equations first. Multiply the top by -1 and then it'll make x=2

Answer 2

Alright, thank you. ^^ I used the top and second, and the second and third to make new equations, haha.

Answer 3

Go for the easiest stuff first. Haha

Answer 4

Okay, so you have x=2. This time, use the first and second equations.

2y-z=5
-y+3z=-10

Multiply the second equation by 2, you get 5z=-15
z=-3

Answer 5

x+2y-z=7 ------- x+2y-z=7
4x-y+3z=-2
2x+2y-z=9 ------2x+2y-z=9
------------- subtraction
-x 0 0 =-2 ----- -x=-2 --- x=2
- than x=2 --- 2+2y-z=7 --- 2y-z=5
8-y+3z=-2 -- -y+3z=-10 --- y=3z+10
- so if y=3z+10 --- than 4+2(3z+10)-z=9 --- 4+6z+20-z=9 --- 5z=-15 ---
--- z=-3
--- 2+2y-(-3)=7 --- 2y+3=5 --- 2y=2 --- y=2/2 =1 --- y=1

x=2
y=1
z=-3

Answer 6

The same thing can be done a bit more systematically as described here:

http://www.okc.cc.ok.us/maustin/Matrix_Solutions/Matrix%20Solution%20of%20Linear%20Systems.htm