3.3 Solving Systems of Inequalities by Graphing

Pg. 123

Standards addressed: 2.1 & 2.2

1. Write the inequality in slope-intercept form.

2. Use the slope and y-intercept to plot two points.

3. Draw in the line. Use a solid line for less than or equal to () or greater than or equal to (). Use a dashed line for less than (<) or greater than (>).

4. Pick a point above the line or below the line. Test that point in the inequality. If it makes the inequality true, then shade the region that contains that point. If the point does not make the inequality true, shade the region on the other side of the line.

5. Systems of inequalities – Follow steps 1-4 for each inequality. Find the region where the solutions to the two inequalities would overlap and this is the region that should be shaded.

Steps for Graphing Inequalities:

Look at the two graphs. Determine the following:

A. The equation of each line.

B. How the graphs are similar.

C. How the graphs are different.

Use a dotted or dashed line when the inequality is < or >

Use a solid line when the inequality is ≤ or ≥

Solutions of Lines Vs. Inequalities

• We can test a solution to a line by picking a point that is on the line and plugging that point back into the equation.

• We can test a solution to an inequality by picking a point that is SOMEWHERE in the shaded region and plugging that point into the inequality.

Pick a point from the shaded region and test that point in the inequality y ≥ x + 3.

Point: (-4, 5)

Pick a point from the shaded region and test that point in the equation y ≤ -x + 4.

Point: (1, -3)

http://www.mathbits.com/MathBits/TISection/Algebra1/linearinequ2.htm

Systems of Equations vs.

Systems of Inequalities

• A system of equations will have ONE point, no points, or an infinite amount of points for an answer. The SOLUTION is where the two lines intersect.

• A system of inequalities will have MANY ordered pairs that satisfy the inequalities.

Heart Rate

Graph the following linear system of inequalities.y x

y x

2 4

3 2

x

y

Use the slope and y-intercept to plot two points for the first inequality.

Draw in the line. For use a solid line.

Pick a point and test it in the inequality. Shade the appropriate region.

Graph the following linear system of inequalities.y x

y x

2 4

3 2y x

2 4 P o in t (0 ,0 )

0 2 (0 ) - 4

0 -4

The region above the line should be shaded.

x

y

Now do the same for the second inequality.

Graph the following linear system of inequalities.y x

y x

2 4

3 2

x

y

Use the slope and y-intercept to plot two points for the second inequality.

Draw in the line. For < use a dashed line.

Pick a point and test it in the inequality. Shade the appropriate region.

Graph the following linear system of inequalities.y x

y x

2 4

3 2

x

y

y x

3 2

3

P o in t (-2 ,-2 )

-2 (-2 ) + 2

-2 < 8

The region below the line should be shaded.

Graph the following linear system of inequalities.y x

y x

2 4

3 2

x

y

The solution to this system of inequalities is the region where the solutions to each inequality overlap. This is the region above or to the left of the green line and below or to the left of the blue line.

Shade in that region.

Graph the following linear systems of inequalities.

1 . y x

y x

4

2

y x

y x

4

2

x

y Use the slope and y-intercept to plot two points for the first inequality.

Draw in the line.

Shade in the appropriate region.

x

y

y x

y x

4

2

Use the slope and y-intercept to plot two points for the second inequality.

Draw in the line.

Shade in the appropriate region.

x

y

y x

y x

4

2

The final solution is the region where the two shaded areas overlap (purple region).

Homework:

• Workbook pg. 16 (1-9 – we will start class next time with number 10.)