Grade 12 Math: Two Variable Inequalities

Two Variable Inequalities

Read each question carefully and provide your answers in the space provided. For graphing questions, clearly shade the solution region.

1. Graph the inequality \(2x - 3y < 6\) on the coordinate plane below. Clearly indicate the boundary line and shade the solution region.

2. Which of the following points is a solution to the inequality \(y \ge -x^2 + 4\)?

3. The boundary line for an inequality with a \(<\) or \(>\) symbol is always a   line.

4. The set of all points that satisfy an inequality is called the   region.

5. Write the inequality represented by the shaded region in the graph below. The boundary line passes through (0, 4) and (4, 0) and is solid. The region below the line is shaded.

6. The inequality \(y < x\) includes the points on the line \(y = x\) in its solution set.

7. A company produces two types of widgets, A and B. Widget A takes 2 hours to produce and widget B takes 3 hours. The company has a maximum of 30 production hours available per day. Let \(x\) be the number of widget A produced and \(y\) be the number of widget B produced. Write an inequality that represents this constraint.

8. If the company must produce at least 5 of widget A and at least 3 of widget B, write two more inequalities to represent these constraints.