a*x+b*y=c

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Solution for a*x+b*y=c equation: 


Simplifying
a * x + b * y = c

Multiply a * x
ax + b * y = c

Multiply b * y
ax + by = c

Solving
ax + by = c

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 = -1by + c

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

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

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

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