Chapter 4: Q 289 (page 472)

In the following exercises, solve each system by graphing.
$\{\begin{cases} y \geq - \frac{2}{3} x + 2 \\ y > 2 x - 3 \end{cases}$

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 system of equations $\{\begin{cases} y \geq - \frac{2}{3} x + 2 \\ y > 2 x - 3 \end{cases}$

Checking the point for system of equation

The equation $y = - \frac{2}{3} x + 2$ has intercept $2, 3$ . Testing the point $(0, 0)$ , we get

$0 \geq 0 + 2 0 \geq 2$ which is not true

So origin is not included

Checking the point for system of equations

The equation $y = 2 x - 3$ has intercept $- 3, \frac{3}{2}$ . Testing the point $(0, 0)$ , we get

$0 > 0 - 3 0 > - 3$ which is not true

So origin is not included

Graphing the system of equations

The graph of the system of equations is

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In the following exercises, solve each system by graphing.
$\{\begin{cases} y \geq - \frac{2}{3} x + 2 \\ y > 2 x - 3 \end{cases}$

Short Answer

Step by step solution

Given information

Checking the point for system of equation

Checking the point for system of equations

Graphing the system of equations

One App. One Place for Learning.

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In the following exercises, solve each system by graphing.y≥-23x+2y>2x-3

Short Answer

Step by step solution

Given information

Checking the point for system of equation

Checking the point for system of equations

Graphing the system of equations

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Mechanics Maths

Decision Maths

Discrete Mathematics

Pure Maths

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Study anywhere. Anytime. Across all devices.

In the following exercises, solve each system by graphing.
$\{\begin{cases} y \geq - \frac{2}{3} x + 2 \\ y > 2 x - 3 \end{cases}$