Algebra Matrix Inverse: Expressing x variables in terms of z variables"

[vg19]

Hey again!
Im having trouble with this problem given in the matrix inverse section of the textbook. It gives these two matricies in the form AX=B
[x1]=[3 -1 2][y1]
[x2]=[1 0 4][y2]
[x3]=[2 1 0][y3]
and
[z1]=[1 -1 1][y1]
[z2]=[2 -3 0][y2]
[z3]=[-1 1 -2][y3]
The question says, given the first matrix and the second matrix, express the variables, x1, x2, x3 in terms of z1, z2, z3. I am not too sure on where to start here. So far, I just multiplied through to find the equations for the x variables and z variables.
x1 = 3y1 - y2 + 2y3
x2 = y1 + 4y3
x2 = 2y1 + y2
z1 = y1 - y2 + y3
z2 = 2y1 - 3y2
z3 = -y1 + y2 + 2y3
Im not sure on where to go from here.
Thanks in advance

 

[HallsofIvy]

If Y= AX and Z= BY then Z=B(AX)= (BA)X and so X= (BA)^-1Z= (A^-1B^-1)Z. Can you find the inverses of those matrices?
(Or multiply them and then find the inverse of the product.)