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Question

# Solve for x,y:(a+2b)x+(2a−b)y=2,(a−2b)x+(2a+b)y=3.

A
x=(5b2a),y=10ab
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B
x=5b2a10ab,y=a+10b10ab
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C
x=5b2a10ab,y=5a+10b10ab
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D
x=5b+2a10ab,y=a+10b10ab
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Solution

## The correct option is B x=5b−2a10ab,y=a+10b10ab(a+2b)x+(2a−b)y=2⇒y=2−ax−2bx2a−b(a−2b)x+(2a+b)y=3⇒(a−2b)x+(2a+b)×2−ax−2bx2a−b=3⇒(ax−2bx)(2a−b)+(2a+b)(2−ax−2bx)2a−b=3⇒2a2x−4abx−abx+2b2x+4a+2b−2a2x−abx−4abx−2b2x=3(2a−b)⇒4a+2b−10abx=6a−3b⇒2a−5b+10abx=0⇒x=5b−2a10aby=2−a(5b−2a10ab)−2b(5b−2a10ab)2a−b⇒y=2(10ab)−a(5b−2a)−2b(5b−2a)10ab×12a−b⇒y=20ab−5ab+2a2−10b2+4ab10ab×(2a−b)⇒y=19ab+2a2−10b210ab×(2a−b)⇒y=a+10b10ab

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