Question

Solve the system of equations using elemination

2x-3y+z=0
2x+y+z=12
y-z= 4

Answer 1

What have you done so far? Do you understand what it's asking you to do?

Answer 2

Not really I've done some problem with 2 equations but not three

Answer 3

It's the same concept but with one more step. You can begin anywhere, but I'll be using equation 3 as it's easiest to rearrange to make a variable the subject.
\[y=4+z\]
We can use this to eliminate y from the other two equations, leaving us with two equations in terms of x and z. Equation 1:
\[0=2x-3(4+z)+z=2x-12-3z+z=2x-2z-12\]\[2x-2z=12\]\[x-z=6\]
Equation 2:
\[12=2x+y+z=2x+(4+z)+z=2x+4+2z\]\[2x+2z=8\]\[x+z=4\]

Solve these two equations for x and z, then use y=4+z to get y.

Answer 4

thank you so much!

Answer 5

My pleasure. If you want to check your answers, I believe it's x=5, y=3, z=-1.