Q. 320 In the following exercises, solv... [FREE SOLUTION]

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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 11: Q. 320 (page 1159)

In the following exercises, solve the system of equations by using elimination.
$x^{2} - y^{2} = 5 - 2 x^{2} - 3 y^{2} = - 30$

Short Answer

Expert verified

Solution

$\begin{matrix} x = 3, 鈥� & y = 2 \end{matrix} \begin{matrix} x = - 3, 鈥� & y = 2 \end{matrix} \begin{matrix} x = 3, 鈥� & y = - 2 \end{matrix} \begin{matrix} x = - 3, 鈥� & y = - 2 \end{matrix} (3, 2) (- 3, 2) (3, - 2) (- 3, - 2)$

Step by step solution

Given Information

Given equations are

$x^{2} - y^{2} = 5 - 2 x^{2} - 3 y^{2} = - 30$

Eliminate a variable 'x'

$x^{2} - y^{2} = 5 - 2 x^{2} - 3 y^{2} = - 30 M u l t i p l y t h e f i r s t e q u a t i o n b y 2 2 x^{2} - 2 y^{2} = 10 - 2 x^{2} - 3 y^{2} = - 30 - - - - - - - - - - - - - - 5 y^{2} = - 20 y^{2} = 4 y = 卤 2$

solve for x

we got y= +2, y=-2

Substitute it in any one of the equation and solve for x

$x^{2} - y^{2} = 5 y = + 2 x^{2} - 2^{2} = 5 x^{2} - 4 = 5 x^{2} = 9 x = 卤 3 (2, 3) a n d (2, - 3) x^{2} - y^{2} = 5 y = - 2 x^{2} - {(- 2)}^{2} = 5 x^{2} - 4 = 5 x^{2} = 9 x = 卤 3 (- 2, 3) a n d (- 2, - 3)$

verify the solution

$(3, 2) x^{2} - y^{2} = 5 {(3)}^{2} - {(2)}^{2} = 5, T r u e - 2 x^{2} - 3 y^{2} = - 30 - 2 {(3)}^{2} - 3 {(2)}^{2} = - 30, t r u e (- 3, 2) x^{2} - y^{2} = 5 {(- 3)}^{2} - {(2)}^{2} = 5, T r u e - 2 x^{2} - 3 y^{2} = - 30 - 2 {(- 3)}^{2} - 3 {(2)}^{2} = - 30, t r u e (3, - 2) x^{2} - y^{2} = 5 {(3)}^{2} - {(- 2)}^{2} = 5, T r u e - 2 x^{2} - 3 y^{2} = - 30 - 2 {(3)}^{2} - 3 {(- 2)}^{2} = - 30, t r u e (- 3, - 2) x^{2} - y^{2} = 5 {(- 3)}^{2} - {(- 2)}^{2} = 5, T r u e - 2 x^{2} - 3 y^{2} = - 30 - 2 {(- 3)}^{2} - 3 {(- 2)}^{2} = - 30, t r u e$

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91影视

In the following exercises, solve the system of equations by using elimination.
$x^{2} - y^{2} = 5 - 2 x^{2} - 3 y^{2} = - 30$

Short Answer

Step by step solution

Given Information

Eliminate a variable 'x'

solve for x

verify the solution

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91影视

In the following exercises, solve the system of equations by using elimination.x2-y2=5-2x2-3y2=-30

Short Answer

Step by step solution

Given Information

Eliminate a variable 'x'

solve for x

verify the solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Mechanics Maths

Pure Maths

Applied Mathematics

Discrete Mathematics

Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises, solve the system of equations by using elimination.
$x^{2} - y^{2} = 5 - 2 x^{2} - 3 y^{2} = - 30$