Ax+By=Csol

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Solution for Ax+By=Csol equation: 


Simplifying
Ax + By = Csol

Solving
xA + yB = losC

Solving for variable 'x'.

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

Add '-1yB' to each side of the equation.
xA + yB + -1yB = losC + -1yB

Combine like terms: yB + -1yB = 0
xA + 0 = losC + -1yB
xA = losC + -1yB

Divide each side by 'A'.
x = losA-1C + -1yA-1B

Simplifying
x = losA-1C + -1yA-1B

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