How do you graph #2x - 3y >=9# and #- x - 4y >=8#?

1 Answer
Nghi N.
Jul 23, 2015

Graph and solve system:
(1) #2x - 3y >= 9#
(2) #-x - 4y >= 8#

Explanation:

Bring the inequalities to standard form:
(1) #2x - 3y - 9 >= 0#
(2) #- x - 4y - 8 >= 0#
First, graph Line (1): 2x - 3y - 9 = 0 by its 2 intercepts.
make x = 0 --> y = -2. Make y = 0 --> #x = 9/2#.
To find the solution set, use the origin O as test point. Substitute x = 0, y = 0 into the inequality (1). We get #-9 >= 0#. Not true. Then, the solution set is the area that doesn't contain O. Color or shade it.
Next, graph the Line (2): -x - 4y - 8 = 0 by its 2 intercepts.
Make x = 0 --> y = -2. Make y = 0 --> x = -8.
Substitute x = 0 and y = 0 into inequality (2). We get #-8 >= 0.# Not true. Then, the solution set is the area that doesn't contain O. Color or shade it.
The compound solution set is the commonly shared area.
graph{2x - 3y - 9 = 0 [-10, 10, -5, 5]}
graph{-x - 4y - 8 = 0 [-10, 10, -5, 5]}
NOTE, The 2 lines (1) and (2) are included in the solution set.

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