/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 66 Explain how to solve a nonlinear... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 66

Explain how to solve a nonlinear system using the addition method. Use \(x^{2}-y^{2}=5\) and \(3 x^{2}-2 y^{2}=19\) to illustrate your explanation.

Short Answer

Expert verified
The solutions for the system of nonlinear equations are \(x = 卤 \sqrt{5.8}\) and \(y = 卤 \sqrt{4/5}\)

Step by step solution

01

Write down the equations

First, present both provided equations: \(x^{2}-y^{2}=5\) and \(3 x^{2}-2 y^{2}=19\)
02

Multiply equations to prepare for addition

To be able to eliminate one variable using addition method, both equations should be written in a way that allows the cancellation of one variable. Multiply the first equation by 2, and the second equation by 1, which yields: \(2x^{2}-2y^{2}=10\) and \(3 x^{2}-2 y^{2}=19\)
03

Add the equations

Now, add the two equations to eliminate \(y^{2}\). The result is \(5x^{2} = 29\), or simplified further \(x^{2} = 29/5\)
04

Solve for x

Take the square root on both sides for solving \(x\). Thus, \(x = \sqrt{29/5} = 卤 \sqrt{5.8}\)
05

Solve for y

Substitute the obtained values of \(x\) into one of the original equations, the first one for instance. You get \(y^{2} = x^{2} - 5 = 5.8 - 5 = 0.8\). Hence, \(y = \sqrt{0.8} = 卤 \sqrt{4/5}\)

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

When an airplane flies with the wind, it travels 800 miles in 4 hours. Against the wind, it takes 5 hours to cover the same distance. Find the plane鈥檚 rate in still air and the rate of the wind.

$$ \text { Let } f(x)=\left\\{\begin{aligned} x+3 & \text { if } x \geq 5 \\ 8 & \text { if } x<5 \end{aligned}\right. $$

Sketch the graph of the solution set for the following system Of inequalities: $$ \left\\{\begin{array}{l} {y \geq n x+b(n<0, b>0)} \\ {y \leq m x+b(m>0, b>0)} \end{array}\right. $$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. The reason that systems of linear inequalities are appropriate for modeling healthy weight is because guidelines give healthy weight ranges, rather than specific weights, for various heights.

The group should write four different word problems that can be solved using a system of linear equations in two variables. All of the problems should be on different topics. The group should turn in the four problems and their algebraic solutions.
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.