Since we are using elimination, we must subtract one equation from another.
Let us solve for x first. We will need to subtract out y completely. Multiplying the equation 7x + y = 6 by 3 yields 21x + 3y = 18. We can subtract 5x + 3y = 34 from it.
21x + 3y = 18
-5x + 3y = 34
= 16x = - 16
Solving for x, x = -1
Plug this into either equation and solve accordingly for y.
5(-1) + 3y = 34
-5 + 3y = 34
3y = 39
y = 13
Your answer should be x = -1 and y = 13. Hope this helps!