Solving Linear Systems

1
Solving Linear Systems

• Solve the system
• y x 2
• y -2x 7
• Group 1 - 3 use graphing
• Group 3 6 use elimination
• Group 7 and 8 use substitution

(3,1)
2
Solving Linear Systems

• Solve the system
• y -x 3
• y 3/2x 2
• Group 1 - 3 use elimination
• Group 3 6 use substitution
• Group 7 and 8 use graphing

(2,1)
3
Solving Linear Systems

• Solve the system
• 2x 4y 12
• x y 2
• Group 1 - 3 use substitution
• Group 3 6 use graphing
• Group 7 and 8 use elimination

(-2, 4)
4
Solving Linear Systems

• Solve the system
• 3 4y x
• 4y -x 3
• Use any method!

Infinite Solutions Dependent System
5
Solving Linear Systems

• Solve the system
• 3x -5y 4
• 250 150x 300y
• Use any method!

(-1/33, 9/11)
6
Solving Linear Systems

• Solve the system
• 7x y 6
• -7x y -6
• Use any method!

Infinite Solutions Dependent
7
Solving Linear Systems

• Solve the system
• x -3
• y 5
• Use any method!

(-3, 5)
8
Solving Linear Systems

• Solve the system
• -3x y 4
• x 1/3y 1
• Use any method!

Inconsistent
9
Solving Linear Systems

• Find the linear models for each set of data. In
  what year will the two quantities be equal?

10
Solving Linear Systems

• Find the linear models for each set of data. In
  what year will the two quantities be equal?

11
Solving Linear Systems

• You and a friend are both reading a book. You
  read 2 pages each minute and have already read 55
  pages. Your friend reads 3 pages each minute and
  has already read 35 pages. Solve the system of
  equations to find when the two of you will have
  read the same number of pages.

12
Solving Linear Systems

• Jennys Bakery sells carrot muffins at 2 each.
  The electricity to run the oven is 120 per day
  and the cost of making carrot muffins is 1.40.
  How many muffins need to be sold each day to
  break even?

13
Solving Linear Systems

• A student has some 1 bills and some 5 bills in
  his wallet. He has a total of 15 bills that are
  worth 47. How many of each type of bill does he
  have?

14
Solving Linear Systems

• A student took 60 minutes to answer a combination
  of 20 mulitple-choice and extended response
  questions. She took 2 minutes to answer each
  multiple choice question (m) and 6 minutes to
  answer each extended response question (r).
• How many of each type of question was on the
  test?

15
Solving Linear Systems

• A scientist wants to make 6 milliliters of a 30
  sulfuric acid solution. The solution is make
  from a combination of a 20 sulfuric acid
  solution and a 50 sulfuric acid solution. How
  many milliliters of each solution must be
  combined to make the 30 solution?

16
Solving Linear Systems

• The equation 3x 4y 2 and which equation below
  form a system with no solutions?
• 2y 1.5x 2 b. 3x 4y 2
• c. 2y 1.5x 1 d. 4y 3x -2