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Question

Solve for x and y:
(a+2b)x+(2ab)y=2,(a2b)x+(2a+b)y=3

A
x=1a+115b,y=12a120b
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B
x=12a+15b,y=1a110b
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C
x=1a15b,y=12a+110b
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D
x=12a15b,y=1a+110b
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Solution

The correct option is D x=12a15b,y=1a+110b
(a+2b)x+(2ab)y=2 ........... (1)
(a2b)x+(2a+b)y=3 ............ (2)

Adding (1) and (2), we get

2ax+4ay=5

2x+4y=5a .......... (3)

Subtracting (2) from (1), we get

4bx2by=1

4x2y=1b ........... (4)

Multiply equation (3) by 2 and subtract (4) from the result,

2(2x+4y)(4x2y)=10a+1b

10y=10a+1b

y=1a+110b ............ (5)

Now, from (3),

2x=5a4y

2x=5a4(1a+110b)

2x=1a25b

x=12a15b .......... (6)

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