/*! 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 37 Solve each system by the method ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 13: Problem 37

Solve each system by the method of your choice. $$\left\\{\begin{array}{l} x^{2}+(y-2)^{2}=4 \\ x^{2}-2 y=0 \end{array}\right.$$

Short Answer

Expert verified
The solutions for the system of equations are \( (x, y) = (\sqrt{8/3}, 4/3) \) and \( (x, y) = (\sqrt{2}, 1) \)

Step by step solution

01

Isolate one variable

From the second equation \( x^{2}-2y=0 \), we can isolate \( x^{2} \) for easier substitution into the first equation. This gives us \( x^2 = 2y \).
02

Substitute the isolated variable into the other equation

Substitute \( x^{2} \) from the second equation into the first equation and simplify: \( x^{2}+(y-2)^{2}=4 \) becomes \( 2y + (y - 2)^2 = 4 \). Simplifying this equation gives \( 3y^2 - 8y + 4 = 0 \).
03

Solve the resulting equation

We can use the quadratic formula to solve for \( y \). This gives \( y = \frac{4}{3} \) and \( y = 1 \).
04

Solve for the other variable

Substitute \( y \) into the equation \( x^2 = 2y \) for both obtained values of \( y \). This gives two pairs of solutions for the system: \( (x, y) = (\sqrt{8/3}, 4/3) \) and \( (x, y) = (\sqrt{2}, 1) \).

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

Indicate whether the graph of each equation is a circle, an ellipse, a hyperbola, or a parabola. Then graph the conic section. $$(x-2)^{2}+(y+1)^{2}=16$$

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. $$x=-3 y^{2}-6 y$$

Find the solution set for each system by graphing both of the system's equations in the same rectangular coordinate system and finding points of intersection. Check all solutions in both equations. $$\left\\{\begin{array}{l}x=(y+2)^{2}-1 \\\ (x-2)^{2}+(y+2)^{2}=1\end{array}\right.$$

Indicate whether the graph of each equation is a circle, an ellipse, a hyperbola, or a parabola. Then graph the conic section. $$x=(y-1)^{2}-4$$

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. $$x=-2 y^{2}+4 y-3$$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Geometry

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

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.