Chapter 11: Q. 14 (page 772)

In Problems 5–24, graph each equation of the system. Then solve the system to find the points of intersection.
$x^{2} + y^{2} = 8; x^{2} + y^{2} + 4 y = 0$

Short Answer

Expert verified

The graph of the system of equations $x^{2} + y^{2} = 8; x^{2} + y^{2} + 4 y = 0$ is:

Step by step solution

Step 1. Given

The system of non-linear equation:

$x^{2} + y^{2} = 8; x^{2} + y^{2} + 4 y = 0$

To graph the equation and to find the point of intersection.

Step 2. Graph the equations

Graph the equations in the same plane.

Step 3. To find the point of intersection.

Substitute the first equation in second equation,

$x^{2} + y^{2} + 4 y = 0 8 + 4 y = 0 4 y = - 8 y = - 2$

Step 2. Find x

Substitute $y = - 2$ in the first equation,

$x^{2} + y^{2} = 8 x^{2} + {(- 2)}^{2} = 8 x^{2} + 4 = 8 x^{2} = 4 x = \pm 2$

The points of intersection are $(2, - 2), (- 2, - 2)$

Step 6. Plot the point of intersection

The graph of the system of non-linear equations with the point of intersection 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 Problems 5–24, graph each equation of the system. Then solve the system to find the points of intersection.
$x^{2} + y^{2} = 8; x^{2} + y^{2} + 4 y = 0$

Short Answer

Step by step solution

Step 1. Given

Step 2. Graph the equations

Step 3. To find the point of intersection.

Step 2. Find x

Step 6. Plot the point of intersection

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Statistics

Probability and Statistics

Pure Maths

Geometry

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In Problems 5–24, graph each equation of the system. Then solve the system to find the points of intersection.x2+y2=8;x2+y2+4y=0

Short Answer

Step by step solution

Step 1. Given

Step 2. Graph the equations

Step 3. To find the point of intersection.

Step 2. Find x

Step 6. Plot the point of intersection

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Statistics

Probability and Statistics

Pure Maths

Geometry

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In Problems 5–24, graph each equation of the system. Then solve the system to find the points of intersection.
$x^{2} + y^{2} = 8; x^{2} + y^{2} + 4 y = 0$