Solve Systems of Linear Inequalities

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# Solve Systems of Linear Inequalities - PowerPoint PPT Presentation

Solve Systems of Linear Inequalities. February 10, 2014 Pages 466-468. 7.6 SOLVE SYSTEMS OF LINEAR INEQUALITIES Students will be able to:. Graph and solve linear inequalities in two variables. Graph the system of inequalities. y > – x – 2. Inequality 1. y < 3 x + 6.

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### Solve Systems of Linear Inequalities

February 10, 2014

Pages 466-468

Graph and solve linear inequalities in two variables.

Graph the system of

inequalities.

y > – x – 2

Inequality 1

y < 3x + 6

Inequality 2

Graph both inequalities in the same coordinate plane. The graph of the system is the intersection of the two half-planes, which is shown as the darker shade of blue.

SOLUTION

?

?

1 > 0 – 2

1≤0 + 6

1 > – 2

1≤ 6

Choose a point in the dark blue region, such as (0, 1). To check this solution, substitute 0 for xand 1 for yinto each inequality.

CHECK

Graph the system

of inequalities.

y > – 1

Inequality 1

x > -2

Inequality 2

x + 2y < 4

Inequality 3

SOLUTION

Graph all three inequalities in the same coordinate plane. The graph of the system is the triangular region shown.

Graph the system of linear inequalities.

3.

y < x – 4

y > – x + 3

Graph the system of linear inequalities.

4.

y > – x + 2

y < 4

x < 3

Graph the system of linear inequalities.

5.

y > – x

y > x – 4

y < 5