How do I graph the solution set of a system?

Question

Graph the solution set of the system:

x-2y (greater then or equal to) 4
y-3x (greater then) 5.

Answer 1

For these, first graph them as if they were lines. For the first inequality, you have

x - 2y >= 4
x - 4 >= 2y
x/2 - 2 >= y

Graph this - your slope is 1/2 and your y-intercept is at -2. Since this is a >= problem, you'd use a solid line. You'd also have to decide which side of the line you shade in - this represents the side where the answers lie. How can you tell? Pick a point on either side of your line - (0, 0) is an easy one. If you plug in (0, 0) into your inequality and it comes out true, then shade in the side of the line that has (0, 0) on it. In this case, you'd have -2 >=0, which is false, so you'd have to shade in the other side of the line.

The same goes with your second inequality:

y - 3x > 5
y > 3x + 5

Graph this - slope is 3 and y-intercept is 5. In this case, since it's a > problem, you'd have to use a dashed line instead of a solid line. Do the same thing here with the test point - plug something in and if it works, shade that side in. Using (0, 0), we have 0 > 5, which again is false, so you'd shade in the other side.

When you're done shading, you should have one area that overlaps as a result of your shading. That overlap is the area that solves both inequalities - the solution to your system of inequalities.