Chapter 4: Q 288 (page 472)

In the following exercises, solve each system by graphing.
$\{\begin{cases} y < 2 x - 1 \\ y \leq - \frac{1}{2} x + 4 \end{cases}$

Short Answer

Expert verified

The darkest region represent the solution to the system of equations and the graph is

Step by step solution

Given information

Given the system of equations $\{\begin{cases} y < 2 x - 1 \\ y \leq - \frac{1}{2} x + 4 \end{cases}$

Graph the system of equations

The equation $y = 2 x - 1$ has intercepts as $- 1, \frac{1}{2}$ . Testing the point $0, 0$ , we get

$0 < 0 - 1 0 < - 1$ which is not true so origin is not included

Checking for another equation

The equation $y = - \frac{1}{2} x + 4$ has intercept $4, 8$ . Testing the point $(0, 0)$ , we get

$0 \leq 0 + 4 0 \leq 4$ which is true so origin is included

Graphing the equation

The graph of the equation is

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In the following exercises, solve each system by graphing.
$\{\begin{cases} y < 2 x - 1 \\ y \leq - \frac{1}{2} x + 4 \end{cases}$

Short Answer

Step by step solution

Given information

Graph the system of equations

Checking for another equation

Graphing the equation

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In the following exercises, solve each system by graphing. y<2x-1y≤-12x+4

Short Answer

Step by step solution

Given information

Graph the system of equations

Checking for another equation

Graphing the equation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Discrete Mathematics

Applied Mathematics

Probability and Statistics

Mechanics Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

In the following exercises, solve each system by graphing.
$\{\begin{cases} y < 2 x - 1 \\ y \leq - \frac{1}{2} x + 4 \end{cases}$