HW #29: p. 148 (1-19)

Aim #30: How do we solve a system of inequalities graphically?Homework: HandoutDo Now: Consider the system of inequalities below:

x + y > 10 y ≤ 2x + 1

a) Does the point (4, 7) make the inequality x + y > 10 true?

b) Does the point (4, 7) make the inequality y ≤ 2x + 1 true?

c) Based on your answers from parts a and b would (4, 7) be a solution to the system of inequalities?

Now, let's solve the system of inequalities graphically.

x + y > 10 y ≤ 2x + 1

a) Represent the solution to this system graphically.

b) Name a point that is a solution to x + y > 10 but not y ≤ 2x + 1.

c) Name a point that is a solution to y ≤ 2x + 1 but not x + y > 10.

d) Name a point that is a solution to both inequalities.

e) Where does the solution to a system of inequalities lie?

1) Solve each system of inequalities graphically.

a) y > 4x - 1 b) 3x + y ≤ 52y < -x + 16 3x + y ≥ 8

c) 2x - y < 3 d) x - y > 54x + 3y ≥ 0 x > -1

e) x + y > 2 f) 2x - y < 1 y ≤ x

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2) Consider the compound sentence below.

x + y > 10 and y = 2x + 1

a) Graph the solution set to both x + y > 10 and y = 2x + 1.

b) Describe the solution set to x + y > 10 and y = 2x + 1.

4x + 8y > 16

3) Given: y + x > 2y ≤ 3x - 2

Which graph shows the solution of the given set of inequalities?

4) State if each point is a solution to the system of inequalities illustrated in the graph below.

a) (7, 0)

b) (3, 0)

c) (0, 7)

d) (6, -7)

Sum it Up!The solution to a system of inequalities can be found on a graph by identifying where the shading _______________.