Graph the solution to this system of inequalities

Question

y-x-3 less than or equal to 0

and 2x + 3y is greater than -6

Answer 1

First, rewrite the two inequalities in slope-intercept form: y=mx+b.

For the first inequality, y-x-3≤0, you can add x and 3 to both sides to get y=x+3.

For the second inequality, 2x+3y>-6, add 2x to both sides and then divide by 3. That will give you y>-2/3x-2,.

Now graph the two inequalities: y≤x+3 and y>-2/3x-2. Since y≤x+3 is not a strict inequality (it has equal to as part of its sign), graph this inequality by drawing a solid line. Any area of the graph under or touching the line is part of the inequality. Graph y>-2/3x-2 with a dashed line, because it is a strict inequality (doesn't contain 'equal to' in the sign). Any area of the graph that is over this line is part of that inequality. Find the area of the graph the two inequalities overlap and shade in the region below y≤x+3 and above y>-2/3x-2. The shaded area is the solution to this problem.