Linear Systems, Equations, Inequalities

Which system of inequalities matches the graph?

• y > 2x - 4
  y < 2

• y < 2x - 4
  y < 2

• y > 2x - 4
  y <  2 

• y < 2x - 4
  y <   -2

What does the solution of a linear system tell you?

• The slope

• The y-intercept

• The point of intersection

• Graphing and substitution

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

• (0, -6)

• (6, 0)

• (-4, 2)

• (2, -4)

Match: the overlap is on the left!

• y ≤ -3x   and  y ≤ -2x + 4

• y > -3x   and  y > -2x + 4

• y < 3x   and  y > 2x + 4

• y > 3x   and  y < -2x + 4

Is (0,0) a solution to the system?

• Solution

• Not a solution

Which point is a solution?

• (0, 6)

• (-3, 4)

• (1, 0)

• (-4, 3)

David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost$1.50 each and sodas cost $0.50 each. At the end of the game, David made a total of $78.50 and sold a total of 87 nachos and sodas combined.

• 35 nachos, 52 sodas

• 18 nachos, 69 sodas

• 52 nachos, 35 sodas

• 61 nachos, 26 sodas

Write the system of inequalities
Carlos works at a movie theater selling tickets. The theater has 300 seats and charges $7.50 for adults and $5.50 for children. The theater expects to make at least $2000 for each showing

• x+y≤300
  7.5x+5.5y≥2000

• x+y<300
  7.5x+5.5y≥2000

• x+y≤300
  7.5x+5.5y≤2000

• x+y>2000
  7.5x+5.5y≤300

Which system of inequalities matches the graph?

• x> -2
  y < -4

• x< 2
  y> 4

• x >  2
  y <  4  

• x > 2
  y <- 4

What is the solution to this system of equations?

• Infinite Solutions

• One Solution

• No Solution

• (0, 0)