Review of Systems of Linear Equations

If a system of linear equations has one solution, what does this mean about the two lines?

• Parallel lines

• the same line

• Intersecting lines

Solve the following system of equations by graphing:

• (4, -4)

• (-4, 4)

• no solutions

• (0, 0)

Solve the following system of equations by graphing:

• Infinite solutions

• (2, -2)

• (1, 0)

• (3, -4)

At a restaurant the cost for a breakfast taco and a small glass of milk is $2.10. The cost for 2 tacos and 3 small glasses of milk is $5.15. If a system of equations is written, which would be the correct representation of the 2 variables?

• t: # of tacos

  m: # of glasses of milk

• t: Cost of each taco

  m: Cost of each glass of milk

• t: total cost

  m: # of food items

• t: Cost of each glass of milk

  m: Cost of each taco

Solve using substitution.
x - 2y = 2
3x + 4y = 3

• (1.4, -0.3)

• (3.1, 5)

• (-2.5, 3.5)

• (6.9, 1.02)

This system has _____ solutions

• 0

• 1

• 2

• Infinitely many

Solve the system of equations.
x + 2y = -3
x - y = -12

• (-9, 3)

• (-7 ,5)

• (3, 15)

• (9, 6)

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

• (1,3)

• (1,-3)
  

• (1,1)

• (8,0)

Solve for x and y.
y = 2/3x - 2
y = -x + 3

• (0,3)

• (0,-3)

• (3,0)

• (-3,0)