Download 3-3 Solving Systems of Inequalities by Graphing

3-3 Solving Systems of Inequalities
by Graphing
SWBAT:
• 
Solve Systems if Inequalities by Graphing
Recall: What is a Linear Inequality in Two
Variables?
A Linear Inequality is very
similar in form to Linear
Equations.
}  Where a solution to a
Linear Equation is a
coordinate, so is a solution
to a Linear Inequality
} 
} 
Linear Equations
} 
} 
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2x + 3y = 6
y = ​1/2 x – 3
y=4
Linear Inequalities
} 
} 
} 
2x + 3y < 6
y > ​1/2 x – 3
y≥4
Check Solutions of 2x – 3y ≥ - 2.
1. 
2. 
(0 , 0)
2x – 3y ≥ - 2
2(0) – 3(0) ≥ - 2
0 ≥-2
SOLUTION!
(0 , 1)
2x – 3y ≥ - 2
2(0) – 3(1) ≥ - 2
-3 ≥ - 2
NO SOLUTION!
3. 
4. 
(0 , -1)
2x – 3y ≥ - 2
2(0) – 3(-1) ≥ - 2
3 ≥-2
SOLUTION!
(2 , -1)
2x – 3y ≥ - 2
2(2) – 3(-1) ≥ - 2
7 ≥-2
SOLUTION!
Lets look at a graph of 2x – 3y ≥ - 2
}  Notice
how the solutions of our inequality
are underneath the line…
}  The one non-solution is above our graphed
line…
Lets look at a graph of 2x – 3y ≥ - 2
Any Coordinate that is in that Blue Shaded area
would be a Solution to the Inequality.
}  What do you think about any coordinate in the
white section?
}  What about on the line?
} 
Graphing a Linear Inequalities…
Step 1: Write the Inequality in Slope Intercept form.
Graph the Inequality. Use a Dashed Line for < or >
and a Solid Line for ≥ or ≤.
Step 2: Test the Coordinates of a point in one of the
sections of the Graph.
Step 3: Shade the half of the graph where the
coordinate is if it is a solution to the inequality.
If it is not a solution shade the other side of the
graph.
Use Slope Intercept Form
} 
Graph the inequality x + y > 3
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Pick a coordinate.
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First Write in Slope Intercept Form (minus x from both sides)
y > -x +3 (graph the equation y = -x + 3)
Pick any value not on the line.
See if it is a solution.
} 
} 
Shade the side the coordinate is on if
it is a solution to the inequality,
Shade the other side if it doesn’t.
Use Slope Intercept Form
} 
Graph the inequality 2x – y ≥ -2
} 
} 
} 
Pick a coordinate.
} 
} 
First Write in SI Form (minus 2x from both sides, divide by -1)
y ≤ 2x +2 (Graph the equation y = 2x + 2)
Pick any value not on the line.
See if it is a solution.
} 
} 
Shade the side the coordinate is on if
it is a solution to the inequality,
Shade the other side if it doesn’t.
Graph a Vertical Line
} 
Graph the inequality x < -2
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Pick a coordinate.
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Think about the equation x = -2
Pick any value not on the line.
See if it is a solution.
} 
} 
Shade the side the coordinate is on if
it is a solution to the inequality,
Shade the other side if it doesn’t.
Graph a Horizontal Line
} 
Graph the inequality y ≤ 1
} 
} 
Pick a coordinate.
} 
} 
Think about the equation y = 1
Pick any value not on the line.
See if it is a solution.
} 
} 
Shade the side the coordinate is on if
it is a solution to the inequality,
Shade the other side if it doesn’t.
Graphing Systems of Linear
To Solve a System of Inequalities, we need to find the
ordered pairs that satisfy all the inequalities in the system.
}  One way to solve a system is to graph the inequalities on
the coordinate plane.
}  The solution will be the intersection of the graphs or
where they overlap.
} 
Ex 1: Graph a System of Inequalities
Ex 1B: Graph a System of Inequalities
Ex 1C: Graph a System of Inequalities
Ex 2: Separate Regions
Ex 3: More Inequalities!
x ≤1
y < 2x +1
x + 2y ≥ −4