# How do you graph #x + y >= 2# and #8x - 2y <= 16# and #4y <= 6x + 8#?

##### 1 Answer

Solve system of 3 linear inequalities in 2 variables:

#### Explanation:

Bring all inequalities to standard form

(1)

(2)

(3)

First, graph Line (1) -> x + y - 2 = 0 by its 2 intercepts.

Make x = 0 --> y = 2. Make y = 0 --> x = 2.

Use the origin O as test point. Replace x = 0, y = 0 into (1). We get:

Next, graph Line (2) by its 2 intercepts.

Use O as test point. Replace x = 0 and y = 0 into (2). We get:

Next, graph Line (3) by its 2 intercepts.

Replace x = 0 and y = 0 into (3). We get:

The compound solution set is the triangle area, commonly shared by the 3 solution sets.

graph{x + y - 2 = 0 [-10, 10, -5, 5]}

graph{8x - 2y - 16 = 0 [-10, 10, -5, 5]}

graph{4y - 6x - 8 = 0 [-10, 10, -5, 5]}

Check with point (2, 3) inside the triangle.

(1)

(2)

(3)

NOTE. The 3 lines are included in the solution set because the presence of the sign