well i'm stumped. i can't figure out how to solve this.

Question

solve for (x,y):
3/x + 2/y = 0
5/x - 1/y = 13
i can't graph it, and i can't use a calculator. i keep getting stuck on the second equation b/c i get 5y -13xy -x=0 and since 13 is a prime number i cant figure out what to do next.

Answer 1

first:
3/x + 2/y = 0
times xy
3y + 2x = 0
y = -2x/3

in 2nd:
times xy
5y - x = 13xy
sub in y = -2x/3
5(-2x/3) - x = 13x(-2x/3)
-10x/3 - x = -26x^2/3
times 3
-10x - 3x = -26x^
26x^2 - 13x = 0
13x(2x - 1) = 0
x = 0 or x = 1/2
but x cannot be zero or else we divided by zero in each equation, that would be undefined

x = 1/2
then y = (-2/3)(1/2) = -1/3