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 :

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

Step by step solution

Given information

Two equations are given

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

Eliminate the variable y

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

solve for y

Substitute the x values and find out y

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

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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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

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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

Pure Maths

Applied Mathematics

Logic and Functions

Mechanics Maths

Geometry

Probability and Statistics

Study anywhere. Anytime. Across all devices.

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