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Question

22x+y+15xy=5
55x+y+45xy=14

A
x=8, y=3
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B
x=3, y=8
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C
x=8, y=3
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D
x=8, y=3
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Solution

The correct option is D x=8, y=3

let(1x+y)=uand(1xy)=vthen22u+165v=5(1.)and55+45v=14(2.)multiplyequation(1.)by3,weget66u+45v=15(1.)+55u+45v=14(2.)uponsubtractionof(1.)with(2.),weget11u+0=1u=(111)orx+y=11(3.)andthenv=(522u15)=(5215)=(15)xy=5(4.)add(3.)and(4.)equationweget2x=16x=8andy=11x=118=3


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