9x + 2y = 34
3x + 7y = 5
multiply the bottom equation by 3
9x + 2y = 34
9x + 21y = 15
subtract 2y from both sides on the top and 21y from both sides on the bottom
9x = 34 - 2y
9x = 15 - 21y
see how the 9x is the same in both equations' left parts? That means both equations' right parts are also the same:
34 - 2y = 15 - 21y
34 + 19y = 15
19y = -19
y = -1
3x + 7y = 5
3x + 7(-1) = 5
3x - 7 = 5
3x = 12
x = 4
Answer: x = 4, y = -1