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Algebra IIA
Algebra/Geometry Review: Systems of Equations and Inequalities
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Foundational Material
o Ability to solve one step and multiple step
equations and inequalities
 Goal
o Find solutions that satisfy
systems of equations
o Ability to graph linear equations on a
coordinate plane
o Find solutions that satisfy
systems of inequalities

Why?
o Build a foundation for higher level mathematics
o Solve equations in Economics and Chemistry
o Determine which purchases are better deals

Key Vocabulary
o Consistent system
o Dependent system
o Inconsistent system
o Linear inequality
o System of equations
o Graph one or more
inequalities on a coordinate
plane
o System of
inequalities
o Solution to a system
Lesson 3: Graphing Systems of Inequalities
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Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of
linear equations in two variables. (CC.9-12.REI.6)
Explain why the x-coordinates of the points where the graphs of the equations y=f(x) and y=g(x)
intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using
technology to graph the functions, make tables of values,… (CC.9-12.REI.11)
Create equations in two or more variable to represent relationships between quantities; graph equations
on coordinate axes with labels and scales.* (CC.9-12.CED.2)
Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and
interpret solutions as viable or nonviable options in a modeling context. (CC.9-12.CED.3)
Example #1: Graph y > 2x – 5
When do we use a dotted line?
When do we use a solid line?
When do we shade above the line?
When do we shade below the line?
Solution will be the set of ordered pairs that
satisfy all the inequalities!
Example #2
Example #3
Graph the system:
Plot the graph of the system of inequalities.
y > 2x – 5
1
y   x3
3
3 x  2 y  12
-2x+5y > -10
x  y  1
Is it possible for there to be no solution? If so, describe what the graphs would look like.
Example #4
Plot the graph of the system of inequalities.
2 x6
y  -1
x – 2y > -6
1
y  5   ( x  4)
2
Solve the system by graphing.
1) 2x – y = 10
x + 3y = -9
Solve the system by substitution.
2) 4x + y = -10
-3x + 5y = 19
Solve the system by elimination.
3) 2x – 4y = 5
3x – 6y = 8
Solve the problems that follow.
1. The difference between two numbers is 16.
Three times the larger number is 9 times the
smaller. What are the numbers?
2. Soybean meal is 16% protein and corn meal
is 9% protein. How many pounds of each
should be mixed together to get a 350 lb
mixture that is 12% protein?
3. One canned juice drink is 15% orange juice
and another is 5% orange juice. How many
liters of each should be mixed together to
get a 10 L solution that is 10% orange juice?
4. One day a store sold 30 sweatshirts. White
ones cost $9.95 and yellow ones cost
$10.50. In all, $310.60 worth of sweatshirts
were sold. How many of each color were
sold?