Systems of Equations One Solution No Solution or Infinite Solutions

If a system of linear equations has one solution, what does this mean about the two lines?

• Parallel lines

• the same line

• Intersecting lines

What is the solution to the system?

• (0, 3)

• (1, -1)

• (-3, 1)

• (1, 3)

What is the solution to the system?

• (3, -1)

• (2, -6)

• No Solution 

• (6, -2)

Solve by inspection

y= ¾ x + 5

y= ¾ x + 2

• No Solution

• One Solution

• Infinitely Many Solutions

solve by inspection

y= ¾ x + 5

y= -¾ x + 5

• No Solution

• One Solution

• Infinitely Many Solutions

• No Solution

• One Solution

• Infinitely Many Solutions

Jane is practicing solving systems of equations by inspection. She thinks that y = 5/6x + 2 and y = 5/6x – 2 would have exactly one solution. Is she correct? Why or why not?

Evaluate responses using AI:

OFF

Does the system have one, none or infinite solutions?

y = 2x -11

y = 2x +5

• One

• None

• Infinitely many solutions

How many solutions will this system have? 

• No solution

• One Solution

• I Don't Know

• Infinitely Many Solutions

Based on the equations for each line, determine how many solutions the system would have.

y=-3x+2

y=3x-2

• Infinite Number of Solutions

• No Solution

• One Solution