ax+by=c-x

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Solution for ax+by=c-x equation: 


Simplifying
ax + by = c + -1x

Solving
ax + by = c + -1x

Solving for variable 'a'.

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

Add '-1by' to each side of the equation.
ax + by + -1by = c + -1by + -1x

Combine like terms: by + -1by = 0
ax + 0 = c + -1by + -1x
ax = c + -1by + -1x

Reorder the terms:
ax = -1by + c + -1x

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

Simplifying
a = -1bx-1y + cx-1 + -1

Reorder the terms:
a = -1 + -1bx-1y + cx-1

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