SOLUTION: Solve the system: { 2y - 3x = 13xy { 5y + 2x = 4xy

Algebra ->  Systems-of-equations -> SOLUTION: Solve the system: { 2y - 3x = 13xy { 5y + 2x = 4xy      Log On


   

Question 1101023: Solve the system:
{ 2y - 3x = 13xy
{ 5y + 2x = 4xy
Found 2 solutions by josgarithmetic, KMST:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!

Multiply first by 2 and multiply second equation by 3.
system%284y-6x=26xy%2C15y%2B6x=12xy%29

19y=38xy
y=2xy
2xy-y=0
y%282x-1%29=0
and you can try x=1%2F2 and solve for y using this.
(Seems to give y=-1%2F3 from both original equations)

(Might have one more solution)

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!

There are two ways that
19y=38xy could be true: system%28y=0%2C%22or%22%2Cx=1%2F2%29 .
So, we can see two solutions:
system%28y=0%2C5y%2B2x=4xy%29 --> system%28y=0%2C0%2B2x=0y%29 --> highlight%28system%28y=0%2Cx=0%29%29
system%28x=1%2F2%2C5y%2B2x=4xy%29 --> system%28x=1%2F2%2C5y%2B1=2y%29 --> system%28x=1%2F2%2C3y%2B1=0%29 --> highlight%28system%28x=1%2F2%2Cy=-1%2F3%29%29
Those are solutions.
Could there be another solution?
Does this make sense?
2y-3x=13xy --> 2y-13xy=3x --> %282-13x%29y=3x --> y=3x%2F%282-13x%29
5y%2B2x=4xy --> 5y-4xy=-2x --> %285-4x%29y=-2x --> y=-2x%2F%285-4x%29
We could graph those two rational functions
and their horizontal and vertical asymptotes:

It looks like we've got all the solutions.