/*! 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 35 Solve each system by the method ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 13: Problem 35

Solve each system by the method of your choice. $$\left\\{\begin{array}{l} x^{3}+y=0 \\ x^{2}-y=0 \end{array}\right.$$

Short Answer

Expert verified
The solution to the system is \(x = 0, y = 0\) and \(x = -1, y = 1\).

Step by step solution

01

Express y in terms of x using the second equation

From the second equation, we get \(y = x^2\).
02

Substitute y in the first equation

Substitute y from the first step into the first equation, this gives us a new equation \(x^3 + x^2 = 0\).
03

Solve the resulting equation for x

The equation from step 2 is a quadratic equation, which can be factorized as \(x^2 * (x + 1) = 0\). The solution to this equation is \(x = 0\) or \(x = -1\).
04

Solve for y

Substitute the x values found into the equation \(y = x^2\) to get the corresponding y values. For \(x = 0\), \(y = 0\) and for \(x = -1\), \(y = 1\).

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

Use the vertex and intercepts to sketch the graph of each equation. If needed, find additional points on the parabola by choosing values of y on each side of the axis of symmetry. $$x=-2 y^{2}-4 y+1$$

Indicate whether the graph of each equation is a circle, an ellipse, a hyperbola, or a parabola. Then graph the conic section. $$x^{2}+4 y^{2}=16$$

The equation of a parabola is given. Determine: a. if the parabola is horizontal or vertical. b. the way the parabola opens. c. the vertex. $$y=2(x-1)^{2}+2$$

Indicate whether the graph of each equation is a circle, an ellipse, a hyperbola, or a parabola. Then graph the conic section. $$x^{2}-4 y^{2}=16$$

Indicate whether the graph of each equation is a circle, an ellipse, a hyperbola, or a parabola. Then graph the conic section. $$4 x^{2}+4 y^{2}=16$$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Pure Maths

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

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.