System of Linear Equations and Inequalities

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

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 for x and y.
y = 2/3x - 2
y = -x + 3

• (0,3)

• (0,-3)

• (3,0)

• (-3,0)

7x+4y =12 
x + 2y = -4

• (-4,4)

• (4,4)

• (4,-4)

• (-4,-4)

Which inequality is shown in the graph?

• y < 2x + 1

• y < -2x + 1

• y ≤ 2x + 1

• y ≤ -2x + 1

Match

• y < x−2 
  y < 3

• y > -x+2
  y > 3

• y < -x+2
  y < 3

• y < -x+2
  y > 3

For the system of inequalities below, which ordered pairs are not solutions? Select all that apply.

• (2, 0)

• (0, -5)

• (3, 10)

• (5, 10)

• (5, 0)

Karen makes $5 per hour babysitting and $12 per hour giving music lessons. One weekend, she worked a total of 18 hours and made $139. How many hours did she spend babysitting?

• 4 hours

• 7 hours

• 11 hours

• 18 hours

Two numbers have a sum of 217 and a difference of 85. What is the larger of the two numbers?