3'1 Solving Systems of Equations Graphing

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3.1Solving Systems of EquationsGraphing
Substitution

• Date __________

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Pam has 120 and is spending 5 every
week. Lorenzo has 20 and is saving 7.50 every
week. When will they have the same amount of
money?
Let x of weeks
Let y total money
120 100 80 60 40 20 0
Pam
Lorenzo
total money
In 8 weeks
0 2 4 6 8 10
weeks
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System of Equations

• two or more equations involving the same
  variables
• Solutions are an ordered pair

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No
Yes
Solution must work in both equations!
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Solving Systems by Graphing
Check your answer by plugging the point into both
original equations.
y 2x 1 3 2(2) 1 3 4 1 3 3
x y 5 2 3 5 5 5
(2,3) is the solution!
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3 Possible Outcomes
Independent System
Inconsistent System
Dependent System
Lines Intersect
Lines Parallel
Lines Coincide
One Solution
No Solution
Infinite Solutions
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Solve the system graphically.
One Solution
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Infinitely Many Solutions
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Solve the system graphically, by substitution,
and by elimination.
No Solution
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Substitution Method
Solution is (2, 4)
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Substitution
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Solve using substitution.
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Solve using substitution.
Solve the 1st equation for x.
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Solve using substitution.
Solve the 2nd equation for y.
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Solve using substitution.
Solve 1st equation for x.