GRAPH LINEAR INEQUALITIES IN TWO

VARIABLES

January 23, 2014

Pages 405-408

SOLUTION

Which ordered pair is not a solution of x – 3y ≤ 6?

A (0, 0) B (6, – 1) C (10, 3) D (– 1, 2)

Check whether each ordered pair is a solution of the inequality.

Test (0, 0): x – 3y ≤ 6

0 – 3(0) ≤ 6

Write inequality.

Substitute 0 for x and 0 for y.

Simplify.0 ≤ 6

Test (6, – 1): x – 3y ≤ 6

6 – 3(– 1) ≤ 6 Substitute 6 for x and – 1 for y.

Write inequality.

Simplify.

So, (0, 0) is a solution of x – 3y ≤ 6 but (6, – 1) is not a solution.

ANSWER

The correct answer is B. A B C D

9 ≤ 6

SOLUTION

Tell whether the ordered pair is a solution of – x + 2y < 8.

Check whether each ordered pair is a solution of the inequality.

Test (0, 0 ) – x + 2y < 8.

0 + 2(0) < 8

Write inequality.

Substitute 0 for x and 0 for y.

Simplify.

(0, 0)

0 < 8ANSWER

So, (0, 0) is a solution of – x + 2y < 8.

Graph the inequality y > 4x – 3.

SOLUTION

Graph the equation y = 4x – 3. The inequality is >, so use a dashed line.

STEP 1

STEP 2

0 > 4(0) – 3?

Test (0, 0) in y > 4x – 3.

0 >–3

Shade the half-plane that contains (0, 0), because (0, 0) is a solution of the inequality.

STEP 3

Graph the inequality x + 2y ≤ 0

SOLUTION

STEP 1Graph the equation x + 2y = 0. The inequality is < , so use a solid line.

STEP 2

Test (1, 0) in x + 2y ≤ 01 ≤ 01 + 2(0) ≤ 0

?

Shade the half-plane that does not contain (1, 0), because (1, 0) is not a solution of the inequality.

STEP 3

Graph the inequality x + 3y ≥ –1

SOLUTION

STEP 1Graph the equation x + 3y = –1. The inequality is < , so use a solid line.

STEP 2

Test (1, 0) in x + 3y ≤ –1

1 + 2(0) ≤ –1?

1 ≤ –1

STEP 3

Shade the half-plane that contain (1, 0), because (1, 0) is a solution of the inequality.

HOMEWORK

WORKSHEET P 6.7