Systems of Linear 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)
• (0, 1)

How many solutions does this system of equations have?

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

Determine if (4, 1) is a solution for the system of equations.
y = -x + 5
y = 2x - 7

• yes
• no

Give the solution to the system.

• (3,1)
• (1,3)
• (-1,3)
• (1, -3)

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

• Parallel lines
• the same line 
• Intersecting lines

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. 

Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes.  Which system of equations represents the situation?

• 3x + 2y = 315

  2x + 4y = 450

• 3x + 2y = 450

  2x + 4y = 315

• 2x + 2y = 315

  3x + 4y = 450

Solve the system given:
3x - y = 7
2x + y = 3

• (-1,2)
• (5,4)
• (4,5)
• (2,-1)