Chapter 4: Q 292 (page 472)

In the following exercises, solve each system by graphing $\{\begin{cases} 3 x - y \geq 6 \\ y \geq - \frac{1}{2} x \end{cases}$

Short Answer

Expert verified

The darkest region represent the solution to the system of equation

Step by step solution

Given information

Given the system of equations $\{\begin{cases} 3 x - y \geq 6 \\ y \geq - \frac{1}{2} x \end{cases}$

Checking the point for the system of equations

The equation $3 x - y = 6$ has intercept $- 6, 2$ . Testing the point $(0, 0)$ , we get

$3 (0) - 0 \geq 6 0 - 0 \geq 6 0 \geq 6$ which is not true

So origin is not included

Checking for another equation

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

$0 \geq - \frac{1}{2} (0) 0 \geq 0$ which is true

So origin is included

Graphing the equation

The graph of the equation is

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In the following exercises, solve each system by graphing $\{\begin{cases} 3 x - y \geq 6 \\ y \geq - \frac{1}{2} x \end{cases}$

Short Answer

Step by step solution

Given information

Checking the point for 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

Discrete Mathematics

Calculus

Pure Maths

Statistics

Applied Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In the following exercises, solve each system by graphing3x-y≥6y≥-12x

Short Answer

Step by step solution

Given information

Checking the point for 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

Discrete Mathematics

Calculus

Pure Maths

Statistics

Applied Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In the following exercises, solve each system by graphing $\{\begin{cases} 3 x - y \geq 6 \\ y \geq - \frac{1}{2} x \end{cases}$