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)
• (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

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

Give the solution to the system.

• (3,1)
• (1,3)
• (-1,3)
• (1, -3)

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. 

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

• Parallel lines

• the same line

• Intersecting lines

Answer explanation

The only way 2 lines could touch in an infinite number of points is for the two lines to actually be the same line.

The ordered pair that satisfies BOTH equations in the system is called the _____________________

• system of equations
• function
• graph
• solution