Name:
Period:
Mrs. King

7-2 Substitution
Systems of equations can have 3 different types of solutions.
Intersecting Lines Same Line
Date:
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

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Example # 3 Use substitution to solve the system of inequalities.
2x + 2y = 8 and x + y = -2
Homework Pg 379 # 11-20 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

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Homework Pg 385 # 12-18 even Pg 391 # 14-20 even
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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
3 x - 2 b). 2x - y = -3 and 8x - 4y = -12 c). x - 2y = 4 and x - 2y = -2

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7-5 Graphing Systems of Inequalities
REMEMBER ( < and > ) use , ( ≤ and ≥ ) use
( < and ≤ ) shade below , ( > and ≥ ) shade above
Example # 1 Solve the system of inequalities by graphing. y < 2x + 2 and y ≥ -x - 3
Date:
Example # 2. Solve the system of inequalities by graphing. y ≥ -3x + 1 and y ≤ -3x - 2
Homework Pg 379 # 12 - 22 even

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