Question 924358: if x + 4/y = 4 and y + 6/x = 6, then find (x,y)
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! x+4/y=4 multiply each term by y
xy+4=4y-----eq1
y+6/x=6 multiply each term by x
xy+6=6x---eq2
Rearranging eq1, we get:
4y-xy=4 or
y(4-x)=4
y=4/(4-x)----eq1a--- substitute this into eq2:
(4x/(4-x))+6=6x multiply each term by (4-x)
4x+6(4-x)=6x(4-x)
4x+24-6x=24x-6x^2 collecting like terms and rearranging, we get:
6x^2-26x+24=0 divide by 6
x^2-(13/3)x+4=0 a quadratic in standard form and it can be factored
(x-3)(x-4/3)=0
Sooooo
x=3 and
x=4/3
substitute each of these values into eq1a and solve for y:
y=4/(4-3) or y=4
y=4/(4-4/3)=4/((12-4)/3)=12/8=3/2
So when x=3, y=4
when x=4/3, y=3/2
CK
when x=3, y=4 substitute into eq1
12+4=4*4
16=16
when x=4/3, y=3/2
substitute into eq1
(4/3)(3/2)+4=4(3/2)
2+4=12/2=6
6=6
Hope this helps----ptaylor
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