Question

How do you graph the system `4x - 3y<9` and `2x + y>5`?

Answer 1

Graph sysem of linear functions in 2 variables.

Explanation:

Write the 2 functions to standard form:
(1) 4x - 3y - 9 < 0
(2) 2x + y - 5 > 0

First graph the Line (1) -> 4x - 3y - 9 = 0 by its intercepts.
Make x = 0 -> y = - 3. Make y = 0 -> x = 9/4. Find its solution set.
Use origin O as test point. Substitute x = 0 and y = 0 into inequality (1). We get -9 < 0. It is true, then the area, containing O, is the solution set. Shade or color it.
Next, graph Line (2) -> 2x + y - 5 = 0.
x = 0 -> y = 5. Make y = 0 -> x = 5/2.
Use O as test point. Make x = 0 and y = 0 -> -5 > 0. Not true, then O is not in the solution set area. Color or shade it.
The compound solution set is the commonly shared area.
graph{4x - 3y - 9 = 0 [-10, 10, -5, 5]}
graph{2x + y - 5 = 0 [-10, 10, -5, 5]}