Solutions of Linear Inequalities

Recall: an ordered pair solution to a linear inequality lives in the shaded area.

Give one possible ordered pair solution:

Answer explanation

There are many correct answers. Here are just a few possible answers:

Would an ordered pair on a dashed line be a solution?

• Yes

• No

Answer explanation

The dashed line means that we cannot include points on that line as solutions. They do not give a true statement when plugged into the inequality!

Tags

CCSS.HSA.REI.D.12

Check the boxes of solutions to the linear inequality:

 $y>2x+1$  

•  $\left(-7,\ 8\right)$  

•  $\left(0,\ 4\right)$  

•  $\left(5,\ -2\right)$  

•  $\left(7,\ 5\right)$  

Answer explanation

(5, -2) & (7, 5) are not in the shaded area

Is the ordered pair  $\left(1,\ 3\right)$  a solution to the graphed linear inequality? 

• Yes

• No

Answer explanation

(1, 3) is on the dashed line & cannot be included as a solution

Check the boxes of solutions to the linear inequality:

 $5x-3y≥1$  

•  $\left(5,\ 8\right)$  

•  $\left(7,\ 4\right)$  

•  $\left(0,\ -4\right)$  

•  $\left(-1,\ -1\right)$  

Answer explanation

(-1, -1) is not in the shaded area.

Is the ordered pair  $\left(-1,\ -2\right)$  a solution to the graphed linear inequality?

• Yes

• No

Answer explanation

(-1, -2) is on the solid line so it can be included as a solution

Check the boxes of solutions to the linear inequality:

 $2x+y>5$  

•  $\left(0,\ 0\right)$  

•  $\left(-5,\ -2\right)$  

•  $\left(0,\ 5\right)$  

• None of these

•  $\left(2,\ 1\right)$  

Answer explanation

(0, 0) & (-5, -2) are not in the shaded area.

(0, 5) & (2, 1) are both on the dashed line.

Check the boxes of solutions to the linear inequality:

 $x+4y\le8$  

•  $\left(0,\ 0\right)$  

•  $\left(8,\ 0\right)$  

•  $\left(0,\ 2\right)$  

•  $\left(-8,\ 4\right)$  

Answer explanation

(0, 0) is in the shaded area.

(0, 2), (8, 0) & (-8, 4) are all on the solid line.