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Question

Solve for x,y:
(a+2b)x+(2ab)y=2,(a2b)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=5b2a10ab,y=a+10b10ab
(a+2b)x+(2ab)y=2
y=2ax2bx2ab(a2b)x+(2a+b)y=3
(a2b)x+(2a+b)×2ax2bx2ab=3
(ax2bx)(2ab)+(2a+b)(2ax2bx)2ab=3
2a2x4abxabx+2b2x+4a+2b2a2xabx4abx2b2x=3(2ab)
4a+2b10abx=6a3b
2a5b+10abx=0
x=5b2a10aby=2a(5b2a10ab)2b(5b2a10ab)2ab
y=2(10ab)a(5b2a)2b(5b2a)10ab×12ab
y=20ab5ab+2a210b2+4ab10ab×(2ab)
y=19ab+2a210b210ab×(2ab)
y=a+10b10ab

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