# How do you graph the system 2x - 3y > 6 and 5x + 4y < 12?

May 19, 2015

First graph Line (1) by its 2 intercepts. 2x - 3y = 6 graph{2x - 3y = 6 [-10, 10, -5, 5]}
x = 0 -> y = -2
y = 0 -> x = 3
Find the solution set by using the origin O (0, 0) as test point. We get 0 > 6. Not true, then the solution set is below the line (1). Color this area.

Next, graph Line (2) by its 2 intercepts. 5x + 4y = 12 graph{5x + 4y = 12 [-10, 10, -5, 5]}
x = 0 -> y = 3
y = 0 -> x = 12/5.
Find the solution set by using the origin as test point. We get 0 < 12. Not true. Then the solution area is above Line (2). Color this area.

Finally, the combined solution set of the system is the common area of the 2 solution sets.