Systems of Equations and Inequalities Graphing

When you graph the exact same equation twice,

• you will have no solution. 

• you will have one solution.

• you will have infinite solutions. 

• you will graph a giraffe. 

Lesly graphed two lines in order to find the solution to a given system of equations.
What is the solution?

• (-3,-8)

• (-8,-3)

• (3,-8)

• (8,3)

Buzz graphed two lines in order to find the solution to a given system of equations.
What is the solution?

• (-1, 4)

• (1, -4)

• (-4, 1)

• (4, -1)

Find the values of x and y that maximize the objective function P = 3x + 2y for the graph. What is the maximum value?

• maximum value at (5, 4); 32

• maximum value at (0, 8); 16

• maximum value at (9, 0); 27

• maximum value at (0, 0); 0

Write a system of inequalities to represent the solution of the above diagram.

• y ≥ 2x - 6

  y ≤ -0.5x + 4;

  y ≥ -3x - 6;

• y ≤ 2x - 6

  y ≤ -0.5x + 4;

  y ≥ -3x - 6;

• y ≤ 2x - 6

  y ≤ -0.5x + 4;

  y ≥ -3x - 6;

• y ≥ 2x - 6

  y ≤ -0.5x + 4;

  y ≥ -3x - 6;

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

Write the inequality

• y>-5x-3

• y≥-5x-3

• y<-5x-3

• y≤-5x-3

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 of the following inequalities represents the graph? 

• x≤-2
  y≤x-3

• y≤-2
  y≤x-3

• x≥-2
  y≤x-3

• y≥-2
  y≤x-3

Solve for x and y
2x − 3y = −1
 y = x − 1

• (-2,-3)

• (0,-1)

• (3,4)

• (4,3)