First, subtract color(red)(y)y and color(blue)(z)z from each side of the equation to isolate the zz terms while keeping the equation balanced:
xz - color(blue)(z) + y - color(red)(y) = 1 - color(red)(y) + z - color(blue)(z)xz−z+y−y=1−y+z−z
xz - z + 0 = 1 - y + 0xz−z+0=1−y+0
xz - z = 1 - yxz−z=1−y
Next, factor a zz out of each term on the left giving:
z(x - 1) = 1 - yz(x−1)=1−y
Now, divide each side of the equation by color(red)(x - 1)x−1 to solve for zz while keeping the equation balanced:
(z(x - 1))/color(red)(x - 1) = (1 - y)/color(red)(x - 1)z(x−1)x−1=1−yx−1
(zcolor(red)(cancel(color(black)((x - 1)))))/cancel(color(red)(x - 1)) = (1 - y)/(x - 1)
z = (1 - y)/(x - 1)
