Solutions to Linear Systems of Equations

Erin is 3 years younger than twice Alex's age. Their ages combined are 33 years. How old are Alex and Erin. If x=Erin's age and y=Alex's age, choose the system that matches the situation.

• x + y = 33
  y = 2x - 3

• x + y = 33
  x = 2y - 3

• x + y = 33
  x = 3 - 2y

• x + y = 3
  x = 33 - 2y

How many solutions?

• One Solution

• No solution

• Infinitely Many Solutions

How can you tell if a point is a solution to a system?

• It makes the first equation true.

• The (x,y) coordinates satisfy both equations

• It makes logical sense

• It makes neither equation negative

What is the number of solutions to the system of equations?

• No Solution

• Infinitely Many Solutions

• One Solution

• Two Solutions

How many solutions will this system have?

• One

• Two

• No Solution

• Infinitely Many Solutions

• 1 solution

• 2 Solutions

• No Solution

• Infinite Solutions

Why will this system have infinite solutions?

• The equations are both negative.

• The equations are the same.

• They have the same y-intercept but not the same slope.

• They have the same slope but not the same y-intercept.

What is the solution to the system?

• (-1, 3)

• (-3, 1)

• (3, -1)

• (-3, -1)

If a system of linear equations has infinitely many solutions, what does this mean about the two lines? 

• Intersecting lines

• Same line

• Parallel lines

What is the solution to the system of equations?

• No Solution

• (2, 0)

• Infinitely Many Solutions

• (0, 2)