Q. 322 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. 322 (page 1159)

In the following exercises, solve the system of equations by using elimination.
$x^{2} + y^{2} = 14 x^{2} - y^{2} = 16$

Short Answer

Expert verified

Solution :

$(\begin{matrix} x = \sqrt{15}, 鈥� & y = i \\ x = \sqrt{15}, 鈥� & y = - i \\ x = - \sqrt{15}, 鈥� & y = i \\ x = - \sqrt{15}, 鈥� & y = - i \end{matrix}) (\sqrt{15}, i) (\sqrt{15}, - i) (- \sqrt{15}, i) (- \sqrt{15}, - i)$

Step by step solution

Given information

Two equations are given

$x^{2} + y^{2} = 14 x^{2} - y^{2} = 16$

Eliminate the variable y

$x^{2} + y^{2} = 14 x^{2} - y^{2} = 16 - - - - - - - - - 2 x^{2} = 30 x^{2} = 15 x = 卤 \sqrt{15}$

solve for y

Substitute the x values and find out y

$x = - \sqrt{15} {(\sqrt{15})}^{2} + y^{2} = 14 15 + y^{2} = 14 y^{2} = - 1 y = 卤 i x = + \sqrt{15} {(- \sqrt{15})}^{2} + y^{2} = 14 15 + y^{2} = 14 y^{2} = - 1 y = 卤 i$

verify the solutions

$x^{2} + y^{2} = 14 x^{2} - y^{2} = 16 x = \sqrt{15}, y = i {(\sqrt{15})}^{2} + {(i)}^{2} = 14, t r u e {(\sqrt{15})}^{2} - {(i)}^{2} = 16, t r u e x = - \sqrt{15}, y = i {(- \sqrt{15})}^{2} + {(i)}^{2} = 14, t r u e {(- \sqrt{15})}^{2} - {(i)}^{2} = 16, t r u e x = \sqrt{15}, y = - i {(\sqrt{15})}^{2} + {(- i)}^{2} = 14, t r u e {(\sqrt{15})}^{2} - {(- i)}^{2} = 16, t r u e x = - \sqrt{15}, y = - i {(- \sqrt{15})}^{2} + {(- i)}^{2} = 14, t r u e {(- \sqrt{15})}^{2} - {(- i)}^{2} = 16, t r u e$

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91影视

In the following exercises, solve the system of equations by using elimination.
$x^{2} + y^{2} = 14 x^{2} - y^{2} = 16$

Short Answer

Step by step solution

Given information

Eliminate the variable y

solve for y

verify the solutions

One App. One Place for Learning.

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91影视

In the following exercises, solve the system of equations by using elimination.x2+y2=14x2-y2=16

Short Answer

Step by step solution

Given information

Eliminate the variable y

solve for y

verify the solutions

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Applied Mathematics

Probability and Statistics

Geometry

Calculus

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, solve the system of equations by using elimination.
$x^{2} + y^{2} = 14 x^{2} - y^{2} = 16$