Chapter 11: Q. 27 (page 773)

Graph each equation of the system. Then solve the system to find the points of intersection.
$\{\begin{cases} y = 2 x + 1 \\ 2 x^{2} + y^{2} = 1 \end{cases}$

Short Answer

Expert verified

The point of intersection is $(0, 1) & (- \frac{2}{3}, \frac{1}{3})$ .

Step by step solution

Step 1. Given information

$\{\begin{cases} y = 2 x + 1 \\ 2 x^{2} + y^{2} = 1 \end{cases}$

Step 2. Graphing each equation

$y = 2 x + 1$

$2 x^{2} + y^{2} = 1$

Step 3. Calculation of intersection point

$C o n s i d e r, y = 2 x + 1 . . . . . (1) 2 x^{2} + y^{2} = 1 . . . . . (2) N o w s u b s t i t u t i n g t h e v a l u e o f y f r o m e q . 1 i n t o e q . 2 w e g e t 2 x^{2} + {(2 x + 1)}^{2} = 1 2 x^{2} + 4 x^{2} + 4 x + 1 = 1 6 x^{2} + 4 x = 0 x = 0, - \frac{2}{3} N o w s u b s t i t u t i n g v a l u e o f x i n e q . 1 w e g e t y = 2 (0) + 1 y = 1 y = 2 (- \frac{2}{3}) + 1 y = - \frac{1}{3}$

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.

Graph each equation of the system. Then solve the system to find the points of intersection.
$\{\begin{cases} y = 2 x + 1 \\ 2 x^{2} + y^{2} = 1 \end{cases}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Graphing each equation

Step 3. Calculation of intersection point

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Discrete Mathematics

Pure Maths

Statistics

Geometry

Calculus

Study anywhere. Anytime. Across all devices.

Graph each equation of the system. Then solve the system to find the points of intersection.y=2x+12x2+y2=1

Short Answer

Step by step solution

Step 1. Given information

Step 2. Graphing each equation

Step 3. Calculation of intersection point

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Discrete Mathematics

Pure Maths

Statistics

Geometry

Calculus

Study anywhere. Anytime. Across all devices.

Graph each equation of the system. Then solve the system to find the points of intersection.
$\{\begin{cases} y = 2 x + 1 \\ 2 x^{2} + y^{2} = 1 \end{cases}$