Q. 316 In the following exercises, solv... [FREE SOLUTION]

91影视

Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

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

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

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

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

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91影视

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

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91影视

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

Logic and Functions

Geometry

Calculus

Statistics

Decision Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

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