ax-by+cry=z

Solution for ax-by+cry=z equation:

Simplifying
ax + -1by + cry = z

Solving
ax + -1by + cry = z

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add 'by' to each side of the equation.
ax + -1by + by + cry = by + z

Combine like terms: -1by + by = 0
ax + 0 + cry = by + z
ax + cry = by + z

Add '-1cry' to each side of the equation.
ax + cry + -1cry = by + -1cry + z

Combine like terms: cry + -1cry = 0
ax + 0 = by + -1cry + z
ax = by + -1cry + z

Divide each side by 'x'.
a = bx-1y + -1crx-1y + x-1z

Simplifying
a = bx-1y + -1crx-1y + x-1z