Basic System of Equations

How many solutions does the following system of equations have?

• 1

• 0

• Infinitely many

• none

How many solutions does the following system of equations have?

• 1

• 0

• Infinitely many

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

The solution to this system is...

• (4, -2)

• (4, 2)

• (-2, 4) 

• (-4, -2)

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

• system of equations

• function

• graph

• solution 

What is the solution to the system?

• (0, 3)

• (1, -1)

• (-3, 1)

• (1, 3)

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

• intersecting lines

• parallel lines

• skew lines

• intersecting lines

Some students want to order shirts with their school logo. One company charges $9.65 per shirt plus a setup fee of $43. Another company charges $8.40 per shirt plus a $58 fee. Which equation represents the number of shirts when both companies charge the same amount?

• y = 9.65 + x
  y = 8.40 + x

• y = 9.65x + 43
  y = 8.40x + 58

• y =9.65x
  y = 8.40x

• y = 9.65x - 43
  y = 8.40x - 58