Question 1

Which of the following ordered pairs is a solution to the system of inequalities $$\4.9x - y$$ \leq 163\$$ and $$\$$3.7x - y \geq 125\$$?

Accepted Answer

$$(70, 150)$$

Question 2

What is the first step in graphing the solution set of a system of linear inequalities in two variables?

Accepted Answer

Graph each individual inequality as if it were an equation.

Question 3

Given the system $$\y$$ \leq 2x + 3\$$ and $$\$$y \u003e -x + 1\$$, which region represents the solution set?

Accepted Answer

The region below $$\y = 2x + 3$$\$$ and above $$\$$y = -x + 1\.$$

Question 4

If a point $$(x, y)$$ satisfies only one inequality in a system, what can you conclude?

Accepted Answer

It is not a solution to the system.

Question 5

A company wants to keep the number of hours employees work per week between 30 and 40, inclusive. Which system of inequalities models this situation, where $$\h$$\$ is the number of hours worked?

Accepted Answer

$$\30$$ \leq h \leq 40\$

Question 6

Which of the following best describes the solution set of a system of two linear inequalities in two variables?

Accepted Answer

The region where the shaded areas of both inequalities overlap.

Question 7

Suppose you are graphing the system $$\y$$ \u003e 2x - 1\$$ and $$\$$y \leq -x + 4\. $$What type of lines should you use for each inequality?

Accepted Answer

Dashed for $$\y$$ \u003e 2x - 1\$$ and solid for $$\$$y \leq -x + 4\.$$

Question 8

A nutritionist models a healthy weight region for adults using the system $$\4.9x - y$$ \leq 163\$$ and $$\$$3.7x - y \geq 125\$$, where $$\x$$\$$ is height in inches and $$\$$y\ is $$weight in pounds. What does the solution set represent?

Accepted Answer

All height and weight pairs that are considered healthy for adults.

Question 9

Which test point is commonly used to determine which region to shade when graphing a linear inequality, unless the boundary passes through it?

Accepted Answer

$$(0, 0)$$

Question 10

A system of inequalities is given by $$\y$$ \geq 2x - 5\$$ and $$\$$y \u003c -x + 4\. $$Which of the following points is in the solution set?

Accepted Answer

$$(1, 0)$$

Question 11

If the solution set of a system of linear inequalities is empty, what does this mean?

Accepted Answer

There is no point that satisfies all inequalities in the system.

Question 12

A business must keep its monthly expenses $$\E$$\$$ between $$\$$2000\$$ and $$\5000$$\$ inclusive. Which system of inequalities models this?

Accepted Answer

$$\2000$$ \leq E \leq 5000\$

Question 13

Which of the following is NOT a step in graphing a system of linear inequalities?

Accepted Answer

Solving the system by substitution.

Question 14

Given the system $$\y  -x - 2$$\$, which of the following points is NOT in the solution set?

Accepted Answer

$$(1, 4)$$

Question 15

A region on a graph is bounded by $$\y = 2x + 3$$\$$ (dashed) and $$\$$y = -x + 1\ ($$solid). If the system is $$\y$$ \u003c 2x + 3\$$ and $$\$$y \geq -x + 1\$$, which region is shaded?

Accepted Answer

The region below the dashed line and above the solid line.

Question 16

Which of the following statements is true about the solution set of a system of linear inequalities?

Accepted Answer

It is always a region (possibly empty) in the coordinate plane.

Systems of Linear Inequalities

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