Solve and Graph Linear Inequalities in Two Variables

Which of the following is a linear inequality in two variables?

• 𝑥 + 𝑦 = 2

• 𝑥 + 5 > 8

• 3𝑚 + 5𝑛 < 10

• 3𝑞 – 2𝑞 ≠ 6

Which of the following inequalities illustrate “the sum of 𝑥 and 𝑦 is at most 15”?

• 𝑥 + 𝑦 = 15

• 𝑥 + 𝑦 > 15

• 𝑥 + 𝑦 ≤ 15

• 𝑥 + 𝑦 ≥ 15

Which of the following inequality has (5, 1) as a solution?

• 3𝑥 + 𝑦 ≤ 3

• 3𝑥 – 𝑦 ≤ 3

• 3𝑥 – 𝑦 < 15

• 3𝑥 + 𝑦 < 15

For what possible values of 𝑥 and 𝑦 will make the inequality 5𝑥 + 3𝑦 > 12 true?

• ( 0, 3 )

• ( 3, -1 )

• ( 1, 1 )

• ( 3, 0 )

Which of the following inequalities is represented by the given graph?

• 2𝑥 + 2𝑦 > 2

• 3𝑥 + 2𝑦 < 2

• 3𝑥 − 2𝑦 > 2

• 3𝑥 – 2𝑦 < 2

Which is the correct inequality for the shaded region?

• 𝑦 = − 𝑥 − 2

• 𝑦 > −𝑥 − 2

• . 𝑦 < − 𝑥 + 2

• 𝑦 > 𝑥 – 2

Which of the following points satisfy the inequality 𝑦 < 2𝑥 – 3?

• (5, 2)

• (2, 2)

• (2, 5)

• (0, 1)

Which of the following inequalities is represented by the graph?

• 2𝑥 + 3𝑦 ≥ 15

• 2𝑥 + 3𝑦 ≤ 15

• 3𝑥 – 2𝑦 ≥ 15

• 3𝑥 – 2𝑦 ≤ 15

Transform 3𝑥 − 2𝑦 < 7 into slope- intercept form.

• 𝑦 < 3/2 𝑥 + 7/2

• 𝑦 > 3/2 𝑥 + 7/2

• 𝑦 > 3/2 𝑥 − 7/2

• 𝑦 > 2/3 𝑥 − 7/3

In the inequality 4𝑎 + 3𝑏 < 12, what could be the possible value of 𝑎 if 𝑏 = 2?

• 𝑎 > 2/3

• 𝑎 > −3/2

• 𝑎 < 2/3

• 𝑎 < 3/2