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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