Hi. So we had a long test with this question.. I was wondering how to solve it? Coz our teacher didn't discuss the answers.. and most probably we'll have the same type of question during midterms..

Question

Find the Solution Set

9/|2-5x| - 4/y^2-3y = 5
2/|2-5x| + 2/ 3(y^2-3y) = 1/3

thanks!

Answer 1

I think I would eliminate variables.

multiply the first equation by 2/3
multiply the second equation by 4

add the equations.

solve for abs(2-5x), you will have two solutions.

Then, put each of those solutions into the first equation, and solve for y.

Get a large blank pad on which to do this problem, and check it twice. You can finally check each solution by substitution into the second equation.

Answer 2

That's quite nasty for a test.

I would try the following, along the lines suggested by bobpursley

multiply the first by 2
18/|2-5x| - 8/(y^2-3y) = 10
multiply the second by 9
18/|2-5x| + 6/(y^2-3y) = 3
subtract:
-14/(y^2-3y) = 7
7y^2 - 21y + 14 = 0
y^2 - 3y + 2 = 0
(y-2)(y-1) = 0
y = 2 or y = 1

I will do the y=2

If y = 2 , then
9/|2-5x| - 4/-2 = 5
9/|2-5x| = 3
3/|2-5x| = 1
|2-5x| = 3

case1: 2-5x=3
-5x = 1
x = -1/5

case2:
-2 + 5x = 3
5x = 5
x = 1

so two pairs from that part:
(1,2) and (-1/5, 2)

you do the other two solutions, using y = 1