Multiply (1) by 4 and (2) by 7: 24x+28y=20, 28y=35x-98. Substitute for 28y in the first equation:
24x+35x-98=20, 59x=118, so x=2 and 4y=10-14=-4, so y=-1. The lines therefore intersect at (2,-1).
Check: this point should satisfy both equations: (1) 12-7=5; (2) -4=10-14. OK.