Home > Algebra > Linear Inequalities in Two Variables

How do you graph the system #-4x > -24# and #10x+5y<20#?

Answer 1

First graph the lines 4x=24 and 10x+5y=20. The graph of the region would be that lying the left of both 4x=24 and 10x+5y=20. The graph would look like this

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Ethan Adkins

To graph the system -4x > -24 and 10x + 5y < 20:

For the inequality -4x > -24:

Divide both sides by -4 to isolate x: x < 6.
Plot a dashed vertical line at x = 6 on the coordinate plane, indicating that x is less than 6.

For the inequality 10x + 5y < 20:

Rearrange the inequality to isolate y: y < -2x + 4.
Plot the line y = -2x + 4 on the coordinate plane.
Shade the region below the line to represent the inequality y < -2x + 4.

The shaded region below the line y = -2x + 4 and to the left of the dashed line x = 6 represents the solution to the system.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

How do you graph the system #-4x &gt; -24# and #10x+5y&lt;20#?

How do you graph the system #-4x > -24# and #10x+5y<20#?