Systems of Equations

If a system of equations has no solution, what does the graph look like? 

• intersecting lines
• parallel lines
• skew lines
• intersecting lines

What is the solution?

• (1, -1)
• (-1, 1)
• (0, -2)
• (2, 0)

What is the first step in solving this equation? 
5x + 7 = 12

• Divide by 5
• Subtract 5
• Add 7

• Subtract 7

Determine the slope and y-intercept.         y = 3/2x - 3

• slope: -3   y-intercept:  (0, 3/2) 

• slope: 3/2   y-intercept:  (0,3) 
• slope:  3/2  y-intercept:  (0, -3)

• slope: 2/3   y-intercept:  (0,-3) 

What is the solution to the equations below ?

y = 3x + 2

y = 3x - 5

• a. NO Solution because the slopes are the same.

• b. ONE Solution because the slopes are the same.

• c. MANY Solutions because the slopes are the same.

• d. No Solution because the y-intercepts are the same.

Give the solution to the system.

• (3,1)
• (1,3)
• (-1,3)
• (1, -3)

Find the solution to the system.
y = x-6
y = -3x + 2

• (0, -6)
• (6, 0)
• (-4, 2)
• (2, -4)

Parallel Lines never intersect because...

• they have the same slopes. 
• they have the same y-intercept.
• they have different slopes.
• they have different y-intercepts. 

Nancy went to the grocery story. On Monday she purchased 4 apples and 6 bananas for a total of $13. On Wednesday she purchased 3 apples and 7 bananas for a total of $13.50. Which system of equations represents the situation?

• 4x + 6y = 3

  13.5x - 13y = 6

• x + y = 4

  x - y = 6

• 4x + 6y = 13

  3x + 7y = 13.5

• 4x - 6y = 13

  3x - 7y = 13.5

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

• Parallel lines
• the same line 
• Intersecting lines