It looks like the system is
3y + 7=5x
7x - 3y=1
If so, then let's isolate 3y in the first row. We don't need to isolate y itself.
3y+7=5x
3y=5x-7
Then we'll plug this into the 2nd equation.
7x - 3y=1
7x - (3y)=1
7x - (5x-7)=1 ... replace 3y with 5x-7
7x-5x+7 = 1
2x+7 = 1
2x = 1-7
2x = -6
x = -6/2
x = -3
Use this to find y.
3y = 5x-7
3y = 5(-3)-7
3y = -22
y = -22/3
--------------------------------------------
Answer: x = -3 and y = -22/3