Systems of Equations

The solution (x, y) to a system of equations is the point where they...? 

• Run off the graph

• Don't touch

• Intersect

• Exist

How many solutions will this system have?

• One

• Two

• No Solution

• Infinitely Many

Give the solution to the system.

• (3,1)

• (1,3)

• (-1,3)

• (1,-3)

Which system of equations does the graph represent?

• y=−x−4
  y=2x−2

• 
  y=−x+4
  y=2x−4

• y=x−4
  y=−2x−2

• 
  y=x+4
  y=−2x−4

What is the solution to the system?

• (-2,6)

• (6,-2)

• (2,-6)

• (-6,2)

Kevin and Mia are saving up for a new gaming console.

Kevin already has $50 and saves $5 per week.

Mia has $20 but saves $8 per week.

Let x = number of weeks

Let y = Total amount saved

• y = 50x + 5

  y = 20x + 8

• y = 8x + 50

  y = 5x + 20

• y = 50x + 8

  y = 20x + 5

• y = 50 + 5x

  y = 8x + 20

 y= 3x − 7  

 y= 3x + 2 

• One Solution

• No Solution

• Infinitely Many

y=x+3 
y=2x+6

• One Solution

• No Solution

• Infinitely Many

Solution?

• After 20 minutes, both companies charge $15.

• After 15 minutes, both companies charge $20

How many solutions will this system have?

• One Solution

• No Solution

• Infinitely Many