Solve the equations individually. For example, use: y< 3x+1, x>1, and x+y>4.
y<3x+1
x>1
y>-x+4
Draw an x-y axis on a piece of graph paper. Graph the first equation: y<3x+1. Mark the y-intercept one vertical unit above origin point. From that point, count three units above and move one unit to the right. Mark this point. Draw a straight line through both these points, using a ruler. Shade the region left of this line.
Graph the next equation: x>1. Move one horizontal unit to the right of the origin. Mark this point. Use a ruler to draw a straight vertical line through this line. Shade the region to the right of this line.
Graph the next equation: y> -x+4. Mark the y-intercept four vertical units below the origin. From that point, count one unit down and four units to the right. Mark this point. Draw a straight line through both these points, using a ruler. Shade the region right of this line.
Compare the lines and the shaded regions. The region that is shaded by all three equations is the solution. In other words, the points in this region can be plugged into all three equations.