Linear Equations and Systems of Linear Equations

The school’s photographer took pictures of couples at this year’s prom. She charged $3.25 for wallet-size pictures and $10.50 for portrait-size pictures. Crystal and Dan bought a total of 10 pictures for $61.50. Write two equations that would be used to solve the system.

• 10.50w+3.25p=10

  w+p=61.50

• 3.25w+10.50p=10

  w+p=61.50

• 10.50w+3.25p=61.50

  w+p=10

• 3.25w+10.50p=61.50

  w+p=10

Each day Mario prepares a large basket of self-serve tortilla chips in his restaurant. On Monday, 40 adults and 15 children ate 10.8 lb of chips. On Tuesday, 35 adult and 22 children ate 12.29 lb of chips. Write two equations that would be used to solve the system so that Mario would know whether adults or children eat more chips on average.

• 15a-40c=12.29

  35a+22c=10.8

• 40a+15c=10.8

  35a+22c=12.29

• 15a+40c=10.8

  35a-22c=12.29

• 40a+15c=12.29

  35a+22c=10.8

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

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

When you graph the exact same equation twice,

• you will have no solution. 

• you will have one solution.

• you will have infinite solutions. 

• you will graph a giraffe. 

Solve the following system by graphing.  What is the solution?

• (3, -2)

• (3, -3)

• (-3, 2)

• (-3, -2)

What is the solution?

• (1, -1)

• (-1, 1)

• (0, -2)

• (0, 1)

Solve the following system by graphing.  What is the solution?

• Infinite number of solutions

• (3, 3)

• (3, -3)

• (-3, 3)

Which is the graph of y= -x + 2?

• A

• B

• C

• D

What is the equation of this line?

• y = 2x +2

• y = 2x -2

• y = -x + 2

• Cannot be Determined