First solve by elimination: multiply 1st eqn by 4 and add to the 2nd: 5y=(-2x+2x)+(24+1); 5y=25, so y=5. Put y=5 in the second eqn, and solve for x: x=2. Or, if we equate the right-hand side of the two eqns we get: -1/2x+6=2x+1; 5x/2=5, so x=2*5/5=2. What does this mean graphically? The point (2,5) is where the lines defined by the equations intersect.
To draw the graph of the first eqn, mark the intercepts: x=0 y=6, the y intercept, and y=0, x=12, the x intercept. Draw a line through these points.
For the graph of the 2nd eqn, the y intercept is 1 and the x intercept is -1/2. Draw a line through these points. Where the lines cross should be (2,5), the solution to the equations.