Determine the Number of Solutions

How many solutions does the linear system have? 

• One Solution
• No Solution
• Infinitely Many Solutions
• Two Solutions

How many solutions does the linear system have?

• One solution
• No Solution
• Infinitely Many Solutions

The linear system below has...

• exactly two solutions
• exactly one solution
• No solution
• Infinitely many solutions

If two lines have the exact same slope but different y-intercepts, those two lines will

• sometimes  have no solution
• always have no solution
• sometimes have one solution
• always have one solution

Which systems result in NO SOLUTION?

Select ALL that apply

• y = 2x -7

  y = 2x +1

• y= 3x -1

  y= 3x -1

• y= x -9

  y=9x+1

• y= -x +3

  y= -x +8

Which system results in exactly ONE solution?

Select ALL that apply

• y = 5x -1

  y = 5x -1

• y = 2x +4

  y= 2x +1

• y = 2x +4

  y= 3x -2

• y = -x +7

  y = 2x +10

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

• Parallel lines
• the same line 
• Intersecting lines

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

• Intersecting lines
• Same line
• Parallel lines

Does the system have one, none or infinite solutions?
8x + 4y = 12
y = -2x + 3

• (0,3)
• (3,0)
• No solution(parallel lines)
• Infinitely many solutions

Solve for x and y
3x + 2y = 16
7x + y = 19

• (-2,5)
• (-2,-5)
• (2,-5)
• (2,5)