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Solve for x and y. 10x+y+2xy=4 15x+y5xy=2

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Solution

10x+y+2xy=4
15x+y5xy=2
let 1x+y=p and 1xy=q
10p+2q=4(1)
15p5q=2(2)
Equation (1)×5 and Equation (2)×2
50p+10q=2030p10q=480p=16
p=15=1x+y x+y=5(3)
From (1) 2q=410p=42
2q=2
q=1=1xy xy=1(4)
(3)+(4)
2x=6 x=3
y=5x=53=2
x=3 and y=2


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