Math
posted by Jen on .
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..
Find the Solution Set
9/25x  4/y^23y = 5
2/25x + 2/ 3(y^23y) = 1/3
thanks!

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(25x), 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. 
That's quite nasty for a test.
I would try the following, along the lines suggested by bobpursley
multiply the first by 2
18/25x  8/(y^23y) = 10
multiply the second by 9
18/25x + 6/(y^23y) = 3
subtract:
14/(y^23y) = 7
7y^2  21y + 14 = 0
y^2  3y + 2 = 0
(y2)(y1) = 0
y = 2 or y = 1
I will do the y=2
If y = 2 , then
9/25x  4/2 = 5
9/25x = 3
3/25x = 1
25x = 3
case1: 25x=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