Solving Systems of Linear Equations

What is the solution?

• (-4, 2)

• (4, 2)

• (2, -4)

• (2, 4)

On Monday Joe bought 10 cups of coffee and 5 doughnuts for his office at the cost of $16.50. On Tuesday he bought 5 cups of coffee and 10 doughnuts for a total of $14.25. Which equations could be used to determine the cost of the coffee?

• 10c + 5d = 14.25
  5c + 10d = 16.50

• 10c + 5d = 16.50
  5c + 10d = 14.25

• c + d = 10
  5c + 10d = 16.50

• c + d = 5
  5c + 10d = 16.50

Flagship Cinemas sells movie tickets that are $4 for matinees and $7 for regular. One night, the theater sells 578 tickets and collects $3365 in total ticket sales.
Which system best represents the situation?

• 4x + 7y = 578
  x + y = 3365

• 4x + 7y = 3365
  x + y = 578

• 4y + 7x = 578
  x + y = 3365

• 4y + 7x = 3365
  x + y = 578

Solve:
x + y = 4
-5x - 6y = -18

• (6, -2)

• (-6, 10)

• (2, 2)

• (-2, 6)

Which image shows a system of linear equations with no solutions?

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Which image shows a system of linear equations with infinitely many solutions?

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Solve the following system using any method.

y = 2x + 1

y = 4x - 1

• (1,3)

• (-1,-3)

• (-1,3)

• (3,1)

The solution to a system of equations is any ordered pair that makes both equations true. 

• TRUE

• FALSE

You can solve systems using these methods:

• graphing, substitution, and elimination

• rearranging, thinking, and guessing

• only by graphing

Solve the system given:
3x - y = 7
2x + y = 3

• (-1,2)

• (5,4)

• (4,5)

• (2,-1)