/*! 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 2 Solve each system by the substit... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 13: Problem 2

Solve each system by the substitution method. $$\left\\{\begin{array}{l} x-y=-1 \\ y=x^{2}+1 \end{array}\right.$$

Short Answer

Expert verified
The system of equations has no real solutions.

Step by step solution

01

Express x in terms of y

From equation 1, \(x - y = -1\) , we can express x in terms of y by adding y to both sides. This gives us \(x = y + 1\).
02

Substitute x into the second equation

Now that we have x in terms of y, we can substitute this into the second equation, \(y = x^2 + 1\). After substituting, we have \(y = (y+1)^2 + 1\).
03

Simplify the resulting equation

We now have a quadratic equation in terms of y. We can simplify this by expanding the square and collecting like terms. After simplifying, it becomes \(y = y^2 + 2y + 1 + 1\). When this is rearranged, we find \(0 = y^2 + y + 2\).
04

Solve for y

Unfortunately, the quadratic equation \(y^2 + y + 2 = 0\) has no real roots (you can confirm this by attempting to use the quadratic formula). This tells us that the original system of equations has no real solutions.

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

This will help you prepare for the material covered in the first section of the next chapter. Find the product of all positive integers from \(n\) down through 1 for \(n=5\)

Indicate whether the graph of each equation is a circle, an ellipse, a hyperbola, or a parabola. $$3 x^{2}=27+3 y^{2}$$

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. $$4 x^{2}=36+y^{2}$$

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. $$x=(y-3)^{2}-5$$
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

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.