SOLUTION: how do I solve 1/2x+3/5y=17 1/5x+3/4y=17

 = ,   (1)
 = .   (2)

First of all, multiply the equation (1) by 10 (both sides) and the equation (2) by 20 to get off the denominators. You will get an equivalent system

5x +  6y = 170,   (3)
4x + 15y = 340.   (4)

Next multiply the equation (3) by 4 (both sides) and the equation (4) by (-5) and then add. 
By doing this way, you eliminate x and obtain a single equation for y:

24y - 75y = 4*170 - 5*340,   or

-51y = -1020.   

Hence y =  = 20.

Now substitute the found value y = 20 into the equation (3) and find x = 10.