Chapter 7
(Algebra II Chapter 3)
Systems of Equations
and Inequalities
Name:
Period:
Mrs. King
7-2 Substitution
Date:
Systems of equations can have 3 different types of solutions.
Intersecting Lines
Same Line
Parallel Lines
# of solutions
Terminology
Example # 1 Use substitution to solve the system of inequalities.
x = 4y
and
4x - y = 75
1. Solve one equation for x or y
2. Substitute into opposite equation
3. Solve for the variable
4. Substitute answer into original
equation and solve.
5. Write answer as an ordered pair
Example # 2 Use substitution to solve the system of inequalities.
4x + y = 12 and
-2x - 3y = 14
Example # 3
Use substitution to solve the system of inequalities.
2x + 2y = 8
and
x + y = -2
Homework Pg 120 # 13-18 all
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7-3 & 7-4 Elimination
Date:
Example # 1 Use elimination to solve the system of equations.
-3x + 4y = 12
3x - 6y = 18
1. Look for one variable that has the
same coefficient or opposite
signs.
2. If not, multiply one or both
equations to get same number
and opposite signs.
3. Add equations together and solve.
4. Substitute to get other variable.
5. Write answer as an ordered pair.
Example # 3 Use elimination to solve the system of equations.
4x + 2y = 28
4x - 3y = 18
Example # 1 (7-4) Use elimination to solve the system of equations.
2x + y = 23
3x + 2y = 37
Example # 2
Use elimination to solve the system of equations.
4x + 3y = 8
3x - 5y = -23
Homework Pg 120 # 19 - 24 all
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7-1 Solve by graphing
Date:
Example # 2 Graph each system of equation. Then determine whether the system has NO
solution, ONE solution, or INFINITELY MANY solutions. If it has ONE,
name it.
a).
y = x - 4 and y =
1
x-2
3
b). 2x - y = -3 and 8x - 4y = -12
c). x - 2y = 4 and x - 2y = -2
Homework Pg 113 # 13-20 all
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7-5 Graphing Systems of Inequalities
REMEMBER
( < and > ) use
( < and ≤ ) shade below
, ( ≤ and ≥ ) use
, ( > and ≥ ) shade above
Example # 1 Solve the system of inequalities by graphing.
y < 2x + 2 and y ≥ -x - 3
Example # 2. Solve the system of inequalities by graphing.
y ≥ -3x + 1 and y ≤ -3x - 2
Homework Pg 125 # 13-18 all
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