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Question

# Solve for x and y in the following question:2x+2y+12x−y+59=0, 9x+2y+62x−y+4=0

A
x=1,y=2
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B
x=2,y=1
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C
x=2,y=12
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D
x=12,y=2
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Solution

## The correct option is D x=12,y=22x+2y+12x−y+59=0......(1)9x+2y+62x−y+4=0......(2)Let 1x+2y=a and 12x−y=bSubstituting the assumed values in equations 1 and 2, we get: 2a+b=−59 or 18a+9b=−5......(3)and9a+6b=−4......(4)Solving equations (3) and (4) using elimination method:Multiplying equation (4) by 2 and subtracting (3) from it, we get3b=−3 or b=−1⟹2x−y=−1......(5)Substituting b=−1 in (4)9a−6=−4a=29⇒x+2y=92......(6)Solving equations (5) and (6) using elimination method:Multiplying equation (6) by 2 and subtracting (5) from it, we get2x+4y−2x+y=9+1∴y=2Substituting in (5), we getx=12y=2x+1=2.12+1=2

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