Solve the following linear inequality graphically.

Question

x+2y<4
x-y<5

Each inequality is satisfied in a particular region of an x,y plot. The first inequality is satisfied below the line y = -x/2 + 2, for example.

The second inequality is satisfied above the line y = x + 5.

Draw both lines and shade in the areas that the inequalities represent. You will find that the two lines intersect at x=-2, y=3. A wedged shaped region to the left of that point satisfies both inequalities.