Question

How do you solve the system of inequalities `6x + 5y < - 5` and `2x - 5y \geq - 35`?

Answer 1

Solving by graphing the system:
`6x + 5y < - 5` (1)
`2x - 5y >= - 35` (2).
First, graph the 2 lines by axis- intercepts
Line 1 --> 6x + 5y + 5 = 0
Make x = 0 --> y-intercept = - 1
Make y = 0 --> x-intercept = `-5/6`
Line 2 --> 2x - 5y + 35 = 0
Make x = 0 --> y-intercept = 7
Make y = 0 --> x-intercept = `- 35/2`.
Graph Line 1 and Line 2.
The solution set of Line 1 is the area below this Line 1, as for points in this area `6x + 5y < - 5` and as points on the line are excluded, it being an inequality only, it is dashed.
The solution set of Line 2 is the area above this Line 2 , as for points in this area `2x - 5y >= - 35` and as points on the line are included, it being an equality along with inequality only, it is full and not dashed.
The solution set of the system is the commonly shared area. Color or shade it.
graph{6x + 5y + 5 < 0 [-10, 10, -5, 5]}
graph{2x - 5y + 35 >= 0 [-20, 20, -10, 10]}