Question 1031509
Yes, you have the right idea, and yes, working a problem like this via substitution is the hard way...but here goes...doing it as you recommend...
3x+5y=16
5y = -3x + 16 
y = (-3/5)x + 16/5
Now substitute this into the second equation and get
5x - 7((-3/5)x + 16/5) = -4
5x + (21/5)x - 112/5 = -4
Multiply everything by 5 and get
25x + 21x - 112 = -20
46x - 112 = -20
46x = 92
x = 2
Now plug back in to the first one and get
3(2) + 5y = 16
6 + 5y = 16
5y = 10
y = 2
There you are...(2,2)