Warm - Up• Solve the system algebraically:x + ½y = 5

3y – 2x = 6

Chapter 3.3

Solving Systems of Inequalities

by Graphing

Solve a system of inequalities by graphing:

Just like before, in order to graph – you must first rewrite the equations in slope-intercept form

Y=mx + b

1242

23

yx

xy

Graph the first equation

• The first equation is already in slope-intercept form.

• Remember that the line must be solid since the inequality is also equal to

• Then pick a test point:

For example, choose (0,0) since it is not on the line itself. Substitute in for (x,y)

• 0≥3(0)-2 0≥-2 ? Yes

Graph first equation on graph and shade

-8 -6 -4 -2 2 4 6 8

-5

5

x

y

Rewrite Second Equation

• 2x – 4y < 12

• - 4y < - 2x + 12

• y > ½ x - 3

• Pick test point to see what side is shaded.

Graph the second equation on the same graph as the first

-8 -6 -4 -2 2 4 6 8

-5

5

x

y

The solutions lie within the area where the two shadings overlap

You Try!

24

623

yx

yx

First: Rewrite the equations

Second: Graph the equations

Third: Pick a point to decide the shading

Tonight’s Homework:

Page 126 (12-19) ON GRAPH PAPERQuiz – Elimination/Substitution

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