Solving Linear Systems Using Graphing

A large pizza at Palanzio’s Pizzeria costs $6.80 plus $0.90 for each topping. The cost of a large cheese pizza at Guido’s Pizza is $7.30 plus $0.65 for each topping. Which system of equations could be used to find the number of toppings when both companies cost the same amount?

• y = 6.80 + .65x
  y=7.30+.90x

• x + y = 6.80
  x + y = 7.30

• y = 6.80+.90x
  y = 7.30 + .65x

• y + .90x = 6.80
  y + .65x = 7.30

Which system of inequalities matches the graph?

• x> -2
  y < -4

• x< 2
  y> 4

• x >  2
  y <  4  

• x > 2
  y <- 4

2 or more linear equations with the same set of variables

• System

• System of Equations

• Linear Equations

• Quadratic Equations

a solution to a system that results in one x value and one y value that will satisfy both equations 

• No Solution

• One Solution

• Infinite Solutions

• Beyond Solutions

a solution to a system that results in an unlimited amount of x values and an unlimited amount of y values that will satisfy both equations

• No Solution

• One Solution

• Infinite Solutions

• Beyond Solutions

How many solutions will this system have? 

• No solution

• One Solution

• I Don't Know

• Infinitely Many Solutions

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

• Infinite number of solutions

• (3, 3)

• (3, -3)

• (-3, 3)

What is true when solving systems of equations by graphing?

• A set of two linear equations can have two answers

• You don't need to give the ordered pair

• The solution is where the two lines intersect

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. 

^{What is the solution?} 

• 1

• -2

• (1, 2)

• (1, -1)