
The red line is 5x-y=31 and the blue line is 5x+6y=24. They intersect at the solution: x=6, y=-1 (the point (6,-1)).
Subtract one equation from the other to eliminate x: 6y-(-y)=7y=24-31=-7, so 7y=-7, making y=-1. Now plug y=-1 into either equation:
5x-(-1)=31, 5x+1=31, 5x=30, x=6; or, 5x-6=24, 5x=30, x=6. So x=6 and y=-1.