Linear System Solutions Review

Enterprise charges to rent compact cars for a fixed amount per day plus a fixed amount for each mile driven. Batman rented a car for 6 days, drove it 550 miles and spent $337. Superman rented the same car for 3 days, drove for 350 miles and spent $185. Set up the system. Let "d" represent the fixed charge per day and "m" represent the cost per mile.

• 6d + 550m = 337

  3d + 350m = 185

• 6d + 550m = 185

  3d + 350m = 337

• 6m + 550d = 337

  3m + 350d = 185

• 6m + 550d = 185

  3m + 350d = 337

Write a system of equation to solve the following situation.

Two groups of people order food at a restaurant. one group order 4 pizzas and 7 salads for $34.50. The other group orders 8 pizzas and 3 salads for $30.50. Find the cost of each item.

Let p = pizza and s = salad.

• 4p +7s = 30.50 and 8p + 3s = 34.50

  A pizza costs $2. 40 and a salad costs $3.40

• 4p +7s = 34.50 and 8p + 3s = 30.50

  A pizza costs $2. 50 and a salad costs $3.50

• 4p -7s = 34.50 and 8p - 3s = 30.50

  A pizza costs $1.50 and a salad costs $4.50

• 4p +7s = 34.50 and 8p + 3s = 30.50

  A pizza costs $3.50 and a salad costs $2.50

Write the system of equations from the tables.

Hint: find the slope and y-intercept for each table.

What is the solution?

• (5, 11)

• (2, 5)

• (-1, 1)

• (11, 5)

Identify the two equations for the system given in the tables. Select 2 equations.

If a system of equations has no solution, what does the graph look like? 

• intersecting lines

• parallel lines

• skew lines

• intersecting lines

Write the system of equations

What is the solution to this system?

• (1, -1)

• (-1, 1)

• (0, -2)

• (2, 0)

What is the solution to the system?

• (0, 3)

• (1, -1)

• (-3, 1)

• (1, 3)

Solve the following system by setting the two equations equal to each other.  What is the solution?
HINT:  - 1/3x + 4 = 2/3x + 1 and then solve for x.  Once you find x go back and find y.

• Infinite number of solutions

• (3, 3)

• (3, -3)

• (-3, 3)

Solve for x and y
y = 2x + 1
y = 4x - 1

• (1,3)

• (-1,-3)

• (-1,3)

• (3,1)