Practice Problems for Solving Linear Inequalities Prepared by Richard Gill For Mth 04: Intermediate Algebra Tidewater Community College

Practice problems for Lesson 5.3: Systems of Inequalities. Graph the solution set for each system of inequalities. First do the graph yourself, then see the solution on one of the following frames.

Practice problems. Graph the solution set for each system of inequalities. First do the graph yourself, then see the solution on one of the following frames.

x + y < 2 2x - y > 4 The solution to #1. Points in the red region solve x + y < 2. Points in the yellow region solve 2x – y > 4. Points in the double- shaded brown region solve both inequalities simultaneously. 2x – y = 4 x + y = 2

Solution to #2. Points that solve both inequalities lie in the region that is double-shaded. 3x – y > 6 x + 2y < 4 3x – y = 6 x + 2y = 4

Solution to #3. Points that solve both inequalities lie in the region that is double-shaded. 2x – y < 4 x + y > -1 x + y = 1 2x – y = 4y x

Solution to #4. Points that solve both inequalities lie in the region that is double-shaded. Therefore, no solution. 2x + 3y > 6 2x + 3y = 6

The solution to #5. Points in the yellow region solve y >(1/3)x –3. Points in the red region solve y < -(4/3)x + 3. Points in the brown region solve both inequalities. y >(1/3)x –3 y < -(4/3)x + 3 y = (1/3) x - 3 y = -(4/3)x + 3 x y

The solution to #6. Points in the yellow are solve y > -2x + 4. Points in the red are solve y < 2. Points in the brown are solve both inequalities simultaneously. y > -2x + 4 y < 2 y = 2 y = -2x + 4 x

y > -3 This is the solution for #7. Points in the red area satisfy y > -3. Points in the yellow area satisfy Points in the brown region satisfy both inequalities in the system. y =3

y>-2x+3 y < ½ x -2 This is the solution to #8. Points in the yellow region satisfy y > -2x + 3. Points in the red region satisfy y < ½ x – 2. Points in the brown region satisfy both inequalities simultaneously. y = -2x + 3 y = ½ x - 2 x y