Systems of inequalities math homework help

Find the coordinates of the vertices formed by the system of inequalities.

x + y ≤ 9
y ­- 2x ≥ -21
y ≥ -4x + 15

a. (­6, ­-9), (10, ­-1), (2, 7)

b. (­-9,- ­6), (-­1, 10), (7, 2)

c. (­-30, ­-21), (­-6, -9), (6, 15)

d. (­-6, ­-9), (6, ­-3), (-­12, ­-21)

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Find the minimum value of the region formed by the system of equations and functions below.

y ≥ x ­- 3
y ≤ 6 ­- 2x
2x + y ≥ – ­3
f(x, y) = 3x + 4y


a. -12

b. -4.5

c. 9

d. 24

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At What point is the maximum value found in the system of inequalities graphed below for the function f(x, y) = x – 2y?


a. (0, 3)

b. (0, 0)

c. (5, 0)

d. (5, 3)

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At what point is the maximum value found in the system of inequalities graphed below for the function f(x, y) = 4x ­- 3y?


a. (5, 0)

b. (4, 6)

c. (7, 5)

d. (8, 2)

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Choose the system of inequalities whose solution is represented by the graph.


a. x + y > 3; -x + y > ­- 4

b. -x + y ≥ ­-4; x + y ≤ 3

c. -2x + y > ­-4; 2x + y < 3

d. -x + y > -­4; x + y < 3

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Choose the system of inequalities whose solution is represented by the graph.


a. y < ­- 2 ; x < ­- 3

b. y ≤ – ­2 ; x > ­- 3

c. x ≤ ­- 2 ; y > ­- 3

d. x < ­- 3 ; y < ­- 3

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Which point is a solution to the system of inequalities below?

x + 2y ≥ 4
y – 2x < 0


a. (1, 2)

b. (4, 7)

c. (0, 3)

d. (-­1, 1)

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Which point is not a solution to the system of inequalities shown in the graph?


a. (1, -3)

b. (2, 0)

c. (-­4, 2)

d. (0, 0)