SOLUTION: AX+BY=P BX-AY=Q SOLVE FORX&Y

Question 30327: AX+BY=P
BX-AY=Q SOLVE FORX&Y

Answer by mukhopadhyay(490) (Show Source): You can put this solution on YOUR website!
AX+BY=P (multiply both sides by A)
=> A^2X+ABY=AP.... (1)
BX-AY=Q (multiple both sides by B)
=>B^2X-ABY=BQ..... (2)
A^2X+ABY=AP(from 1)
B^2X-ABY=BQ(from 2)
Adding above equations will result in:
A^2X+B^2X = AP+BQ
=> X(A^2+B^2) = AP+BQ
=> X = (AP+BQ)/(A^2+B^2)
You can either follow the same process for Y by multiplying the first original equation with (-B) and second original equation with A; or you can use the substitution method to solve for Y.
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