Question

ax+by=c and bx+ay=1+c find the value of x and y

Answer 1

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Sol : Given equations are ax+by = c --------------(1) and ay+bx = c+1 --------------(2) multiply equation (1) by 'b' and equation (2) by 'a' we get abx+b2y = bc abx +a2y= ac+a (substract) ------------------------------------ ( b2-a2)y = bc - ac -a y = (bc - ac -a) / ( b2-a2) multiply equation (1) by 'a' and equation (2) by 'b' we get a2x+aby = ac aby+b2x = bc+b (substract) --------------------------- (a2- b2)x = (ac-bc -b) x = (ac-bc -b) / (a2- b2) ∴ the values of x and y are (ac-bc -b) / (a2- b2) , (bc - ac -a) / ( b2-a2) .

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