SOLUTION: x+y=7xy, 2x -3y+xy = 0 by both methods elimination and substitution

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Question 884396: x+y=7xy,
2x -3y+xy = 0
by both methods elimination and substitution
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
A solution using Elimination does not seem possible; but substitution should work.

Solve either equation for either variable; and substitute the expression into the other equation. Solve for the remaining variable for its value and solve then for the other variable's value.

x%2By=7xy
x-7xy=-y
x%281-7y%29=-y
x%287y-1%29=y
highlight_green%28x=y%2F%287y-1%29%29
-
The other equation:
2x-3y%2Bxy=0
2%28y%2F%287y-1%29%29%2B3y%2B%28y%2F%287y-1%29%29y=0
2y%2F%287y-1%29%2B3y%2By%5E2%2F%287y-1%29=0, then multiply left and right by 7y-1,
2y%2B3y%287y-1%29%2By%5E2=0
2y%2B21y%5E2-3y%2By%5E2=0
22y%5E2-y=0
y%2822y-1%29=0
y=0 OR y=1%2F22

Continue this for the corresponding values for x....
Use the green-highlighted formula.

You cannot completely separate the x from the y in both equations in order to use Elimination Method.