Linear Systems Point of Intersection

Solve the system of equations

• Infinite solutions

• (2, -2)

• (1, 0)

• (3, -4)

Homer sells tickets for admission to the school play and collects a total of $104. Admission prices are $6 for adults and $4 for children. He sold 21 tickets total. Write a system to represent this situation assuming "a" represents # of adult tickets and "c" represents # of children's tickets.

• a + c = 21

  6a + 4c = 104

• a + c = 104

  6a + 4c = 21

• a + c = 21

  6c + 4a = 104

• a + c = 104

  6c + 4a = 21

A system of two identical (overlapping) lines will have how many solutions?

• One Solution

• Two Solutions

• No Solution

• Infinite Solutions

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 a system of equations to solve the following situation. The sum of twice a number x and three times a number y is 69. The different between four times number x and twice number y is 18. What are the numbers x and y?

• 2x + 3y = 69 and 4x - 2y = 18

  x = 15 and y = 12

• 3x + 2y = 69 and 4x - 2y = 18

  x = 16 and y = 12

• 2x + 3y = 69 and 4x - 2y = 18

  x = 12 and y = 15

• 3x - 2y = 69 and 4x + 2y = 18

  x = -16 and y = 12

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. 

Write the system of equations

A ___________________ is a set of equations with the same variables. Solving a ___________________ means finding one or more solutions that make each of the equations in the system true. A solution to a ___________________ gives a point of intersection of the graphs of the equations in the system.

• System of Equations

• Substitution of Method

• Solution

• Coincide

A __________________ is a point that the graphs of two equations have in common. For example, (3, 4) is a _________________ of the two graphs shown above. Two graphs may have one ___________________, several points of intersection, or no _________________.

• Coincide

• Point of Intersection

• Solution

• Distributive Property