Ax+Gy=J

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Solution for Ax+Gy=J equation: 


Simplifying
Ax + Gy = J

Solving
xA + yG = J

Solving for variable 'x'.

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

Add '-1yG' to each side of the equation.
xA + yG + -1yG = J + -1yG

Combine like terms: yG + -1yG = 0
xA + 0 = J + -1yG
xA = J + -1yG

Divide each side by 'A'.
x = A-1J + -1yA-1G

Simplifying
x = A-1J + -1yA-1G

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