Question

How do you graph the system of linear inequalities `7x+y>0` and `3x-2y<=5`?

Answer 1

`7x + y > 0` (1)
`3x - 2y <= 5` (2)
This is a system of 2 linear inequalities. Solving it means finding its solution set.
First, graph the 2 lines y1 and y2 by the axis intercepts -->
Line y1 --> 7x + y = 0
This Line y1 passes at the origin and it is downward.
Line 2 --> 3x - 2y = 5
When x = 0 --> y-intercept = `- 5/2`
When y = 0 --> x-intercept = `5/3`.
Solve the 2 inequalities by graphing.
The solution set of Inequality (1) is the area above the line y1.
The solution set of Inequality (2) is the area above the Line y2
The combine solution of the system is the area commonly shared
by the 2 solution sets.
Color the combined solution set.
graph{-7x [-10, 10, -5, 5]}
graph{2x - 3y = 5 [-10, 10, -5, 5]}