Chapter 11: Q. 316 (page 1159)

In the following exercises, solve the system of equations by using substitution.
$x^{2} + y^{2} = 4 x - y = 4$

Short Answer

Expert verified

Solution for the system of equations

\begin{matrix} x = 2 + \sqrt{2} i, & y = - 2 + \sqrt{2} i \end{matrix} \begin{matrix} x = 2 - \sqrt{2} i, & y = - 2 - \sqrt{2} i \end{matrix}

Step by step solution

Given Information

System of equations are

$x^{2} + y^{2} = 4 x - y = 4$

use substitution method

$x^{2} + y^{2} = 4 x - y = 4 x - 4 = y S u b s t i t u t e x - 4 f o r y i n f i r s t e q u a t i o n x^{2} + {(x - 4)}^{2} = 4 x^{2} + x^{2} - 8 x + 16 = 4 2 x^{2} - 8 x + 16 - 4 = 0 2 x^{2} - 8 x + 12 = 0 D i v i d e b y 2 x^{2} - 4 x + 6 = 0 a p p l y q u a d r a t i c f o r m u l a x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a} x = \frac{- (- 4) \pm \sqrt{{(- 4)}^{2} - 4 (1) (6)}}{2 (1)} x = \frac{4 \pm \sqrt{- 8}}{2} x = \frac{4 \pm 2 i \sqrt{2}}{2} x = 2 \pm i \sqrt{2} x = 2 - i \sqrt{2} x = 2 + i \sqrt{2}$

Solve for y

substitute the x value and solve for y

y = x - 4 x = 2 - i \sqrt{2} y = (2 - i \sqrt{2}) - 4 y = - 2 - i \sqrt{2} x = 2 + i \sqrt{2} y = (2 + i \sqrt{2}) - 4 y = - 2 + i \sqrt{2}

solution

solution for the given system of equations

$\begin{matrix} x = 2 + \sqrt{2} i, & y = - 2 + \sqrt{2} i \end{matrix} \begin{matrix} x = 2 - \sqrt{2} i, & y = - 2 - \sqrt{2} i \end{matrix}$

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In the following exercises, solve the system of equations by using substitution.
$x^{2} + y^{2} = 4 x - y = 4$

Short Answer

Step by step solution

Given Information

use substitution method

Solve for y

solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Applied Mathematics

Calculus

Mechanics Maths

Discrete Mathematics

Decision Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, solve the system of equations by using substitution.x2+y2=4x-y=4

Short Answer

Step by step solution

Given Information

use substitution method

Solve for y

solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Applied Mathematics

Calculus

Mechanics Maths

Discrete Mathematics

Decision Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, solve the system of equations by using substitution.
$x^{2} + y^{2} = 4 x - y = 4$