Systems of Equations

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• Math Minutes
• Pick up a study guide as you come in.
• Complete 26-29 only in the Math Minutes packet.
  DO NOT GO ON!!!.
• Finished? Work on TCAP Mastery. Its due
  tomorrow! If you would like it checked, have it
  out on your desk.

Must show work on both to receive credit!!!
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Most Missed Test Questions

• Tamara read a newspaper article about the cost of
  attending a university in 2005.
• The average cost to attend a public university
  was about 12,000 per year.
• The average cost to attend a private university
  was about 30,000 per year.
• The author of the article stated that a person
  would save between 40,000 and 50,000 over 4
  years by attending a public university.
• Which statement best describes the authors
  statement?
• It is valid because the total cost over 4 years
  of attending both types of universities is about
  42,000.
• It is invalid because the total cost over 4 years
  of attending both types of universities is about
  168,000.
• It is invalid because the difference in costs
  over 4 years of attending a private university to
  a public university is about 18,000.
• It is invalid because the difference in costs
  over 4 years of attending a private university to
  a public university is about 72,000.
• Most chosen incorrect answer was C

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Most Missed Test Questions

• Most chosen incorrect answer was C
• Why is C incorrect?
• The diagram below shows the location of two
  schools on a map. The length of each grid square
  represents one mile.
• One route requires traveling northeast on Lookout
  Road.
• One route requires traveling east on Broadway and
  north on Main Street.
• What is the approximate difference between these
  routes?

1. 7.6 miles
2. 11.0 miles
3. 19.4 miles
4. 27.0 miles

Lookout Road
Main Street 11 miles
Broadway 16 miles
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Systems of Equations
Mrs. Manley

• How do you find solutions to systems of two
  linear equations in 2 variables?

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Lesson Objective

• Use the substitution method to solve a system of
  linear equations

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A set of linear equations in two variables is
called a system of linear equations.

A solution of such a system is an ordered pair
which is a solution of each equation in the
system.
Example The ordered pair (4, 1) is a solution of
the system since 3(4)
2(1) 14 and 2(4) 5(1) 3.
Example The ordered pair (0, 7) is not a
solution of the system since 3(0)
2(7) 14 but 2(0) 5(7) 35, not 3.
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Systems of linear equations in two variables have
either no solutions, one solution, or infinitely
many solutions.
A system of equations with at least one solution
is consistent. A system with no solutions is
inconsistent.
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Substitution Method
1. Choose one equation and solve for y (choose
the easiest). In other words, change the equation
to slope- intercept form - y mx b. 2.
Substitute the expression that equals y into the
remaining equation for the y variable. 3.
Solve for x. 4. Now, substitute the value
found for x back into either of the original
equations. 5. Solve for y. 6. Write your
solution as a coordinate pair (x,y). 7. Check
your solution (x,y) to be sure it works in both
the original equations.
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Slope-Intercept Formy mx by mx b
y x - 2 y -x - 4
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Examples

• Y 4x 3
• Y x

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Examples

• y -2x 10
• y x 1

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Examples

• y -1/4x 5
• y x 2

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Examples

• y x 1
• y -4x 10

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y mx bax by c
y 2x - 7 -3x 6y 12
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Examples

• 3x 5y 10
• y x 2

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Examples

• -2x y 6
• y -4x - 12

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Examples

• 3x 4y 11
• y 2x

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Examples

• -4x 8y 12
• y -12x 64

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Standard Formax by cax by c
3x y 2 x - 2y 10
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Examples

• -3x 5y 10
• 2x ½y 24

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Examples

• -2x 1/3y 7
• 6x 1/5y -9

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Examples

• 7x 2y -13
• x 2y 11

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Examples

• -4x y 6
• -5x y 21

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Example 1
3x 2y -1 x - y 3
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Example 2
4x 6y 12 6x 9y 36
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Example 3
4x 5y 3 2x - 3y 7
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Example 4
2x y 3 4x 2y 5