SOLUTION: 3/x+1/y=1 2/x+5/y=18

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Question 95364: 3/x+1/y=1
2/x+5/y=18
Found 2 solutions by kiljoy, edjones:
Answer by kiljoy(51) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Linear System solver (using determinant)
Solve:
+system%28+%0D%0A++++3%5Cx+%2B+1%5Cy+=+1%2C%0D%0A++++2%5Cx+%2B+5%5Cy+=+18+%29%0D%0A++

Any system of equations:


has solution

or



(x=-1, y=4}

Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
3/x+1/y=1
2/x+5/y=18
A. Multiply xy times both sides 3y+x=xy
Multiply xy times both sides 2y+5x=18xy
since 18xy is 18 times larger than xy we can make an equation.
2y+5x=18(3y+x)
2y+5x=54y+18x
subtract 5x and 54y from both sides. -52y=13x
divide 13 into both sides x=-4y
Plug -4y into 3y+x=xy and we get 3y-4y=-4y^2
-y=-4y^2
add 4y^2 to both sides. 4y^2-y=0
Quadratic equation: y=0 and y=.25 but since division by 0 in the original equations would occur if y=0 then y=.25 is the only answer.
Substitute .25 for y in 3/x+1/y=1
3/x+1/.25=1
EdJones
3/x+4=1
3/x=-3
3=-3x
x=-1
Check:
Plug -1 and .25 into 2/x+5/y=18
2/-1+5/.25=18
-2+20=18
EdJones