Q. 347 Solve the nonlinear system of eq... [FREE SOLUTION]

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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

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 $(- 3, 0) & (3, 0) .$

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91影视

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

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91影视

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

Probability and Statistics

Discrete Mathematics

Mechanics Maths

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Applied Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

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