Chapter 11: Q. 347 (page 1160)

Solve the nonlinear system of equations using elimination:
$\{\begin{cases} x^{2} + 9 y^{2} = 9 \\ 2 x^{2} - 9 y^{2} = 18 \end{cases}$

Short Answer

Expert verified

The given equation are Ellipse and hyperbola.

Step by step solution

Step 1. Given Information

Given that the equation is $\{\begin{cases} x^{2} + 9 y^{2} = 9 \\ 2 x^{2} - 9 y^{2} = 18 \end{cases} .$

Step 2. Standard form of equation

When $x^{2} & y^{2}$ have same sign but different coefficient. It is an ellipse. When both have different sign and coefficient is hyperbola.

The solution of $x^{2} + 9 y^{2} = 9$ is ellipse and $2 x^{2} - 9 y^{2} = 18$ is hyperbola. On comparing the equation of Ellipse and hyperbola in standard form,

$\frac{x^{2}}{9} + \frac{9 y^{2}}{9} = \frac{9}{9} \frac{x^{2}}{9} + \frac{y^{2}}{1} = 1 a = 3, b = 1 2 x^{2} - 9 y^{2} = 18 \frac{2 x^{2}}{18} - \frac{9 y^{2}}{18} = \frac{18}{18} \frac{x^{2}}{9} - \frac{y^{2}}{2} = 1 a = 3, b = \sqrt{2}$

Thus, the standard form of ellipse is $\frac{x^{2}}{9} + \frac{y^{2}}{9} = 1$ and hyperbola is $\frac{x^{2}}{9} - \frac{y^{2}}{2} = 1 .$

Step 3. Graph of the equation

On drawing the equation,

Step 4. Point of intersection

The ellipse and hyperbola can be intersected at (-3,0) & (3,0). On verifying to substitute in equation,

$x^{2} + 9 y^{2} = 9 {(- 3)}^{2} + 9 {(0)}^{2} = 9 9 = 9 2 x^{2} - 9 y^{2} = 18 2 {(- 3)}^{2} + 9 {(0)}^{2} = 9 18 = 18$

It satisfies both of the equation. The solution are $(- 3, 0) & (3, 0) .$

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.

Solve the nonlinear system of equations using elimination:
$\{\begin{cases} x^{2} + 9 y^{2} = 9 \\ 2 x^{2} - 9 y^{2} = 18 \end{cases}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Standard form of equation

Step 3. Graph of the equation

Step 4. Point of intersection

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Discrete Mathematics

Statistics

Logic and Functions

Probability and Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

Solve the nonlinear system of equations using elimination:x2+9y2=92x2-9y2=18

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Standard form of equation

Step 3. Graph of the equation

Step 4. Point of intersection

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Discrete Mathematics

Statistics

Logic and Functions

Probability and Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

Solve the nonlinear system of equations using elimination:
$\{\begin{cases} x^{2} + 9 y^{2} = 9 \\ 2 x^{2} - 9 y^{2} = 18 \end{cases}$