Question

Y>1/2x+8
Y<-x-1

Solve the following system of intequalities graphing

Answer 1

The attached figure shows the solutions to the system of inequalities

The solution of the system of the inequalities is all points lie on the area of the common shading (red and blue), not on the lines

Explanation:

Let us find two points on each line to draw them

∵ y =
`(1)/(2)` x + 8 is the equation of the line

→ Put x = 0

∵ y =
`(1)/(2)` (0) + 8

∴ y = 8

∴ The point 1st point is (0, 8)

→ Put x = 2

∵ y =
`(1)/(2)` (2) + 8

∴ y = 1 + 8

∴ y = 9

∴ The point 2nd point is (2, 9)

∵ The sign of the inequality is >

∴ The line is a dashed line and the shading area is over the line

The red line and the red shading represent the solutions to the inequality

y >
`(1)/(2)` x + 8

∵ y = -x - 1 is the equation of the line

→ Put x = 0

∵ y = -1(0) - 1

∴ y = 0 - 1

∴ y = -1

∴ The point 1st point is (0, -1)

→ Put x = 2

∵ y = -1(2) - 1

∴ y = -2 - 1

∴ y = -3

∴ The point 2nd point is (2, -3)

∵ The sign of the inequality is <

∴ The line is a dashed line and the shading area is under the line

The blue line and the blue shading represent the solutions to the inequality y < -x - 1

The solution of the system of the inequalities is all points lie on the area of the common shading (red and blue), not on the lines