Q. 319 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. 319 (page 1159)

In the following exercises, solve the system of equations by using elimination.
$x^{2} + y^{2} = 16 x^{2} - 2 y - 1 = 0$

Short Answer

Expert verified

Solution for the system of equations

$(\begin{matrix} x = \sqrt{7}, 鈥� & y = 3 \end{matrix}) (\begin{matrix} x = - \sqrt{7}, 鈥� & y = 3 \end{matrix}) (\begin{matrix} x = 3 i, 鈥� & y = - 5 \end{matrix}) (\begin{matrix} x = - 3 i, 鈥� & y = - 5 \end{matrix})$

Step by step solution

Given Information

System of equations are

$x^{2} + y^{2} = 16 x^{2} - 2 y - 1 = 0$

standard form

We write both the equations in standard form

$x^{2} + y^{2} = 16 x^{2} - 2 y = 1 M u l t i p l y s e c o n d e q u a t i o n b y - 1 a n d a d d b o t h e q u a t i o n s x^{2} + y^{2} = 16 - x^{2} + 2 y = - 1 - - - - - - - - - y^{2} + 2 y = 15 y^{2} + 2 y - 15 = 0 (y + 5) (y - 3) = 0 y + 5 = 0 y = - 5 y - 3 = 0 y = 3$

Step 3: Substitution method

Lets substitute the y values and solve for x

$x^{2} + y^{2} = 16 y = 3 x^{2} + 3^{2} = 16 x^{2} + 9 = 16 x^{2} = 7 x = 卤 \sqrt{7} y = - 5 x^{2} + {(- 5)}^{2} = 16 25 + x^{2} = 16 x^{2} = - 9 x = 卤 3 i$

Solutions are

Check the solution

Now we need to verify the solution

$(\begin{matrix} x = \sqrt{7}, 鈥� & y = 3 \end{matrix}) x^{2} + y^{2} = 16 {\sqrt{7}}^{2} + 3^{2} = 16, T r u e x^{2} - 2 y - 1 = 0 {\sqrt{7}}^{2} - 2 (3) - 1 = 0, T r u e (\begin{matrix} x = - \sqrt{7}, 鈥� & y = 3 \end{matrix}) x^{2} + y^{2} = 16 {(- \sqrt{7})}^{2} + 3^{2} = 16, T r u e x^{2} - 2 y - 1 = 0 {(- \sqrt{7})}^{2} - 2 (3) - 1 = 0, T r u e (\begin{matrix} x = 3 i, 鈥� & y = - 5 \end{matrix}) x^{2} + y^{2} = 16 {(3 i)}^{2} + {(- 5)}^{2} = 16, T r u e x^{2} - 2 y - 1 = 0 {(3 i)}^{2} - 2 (- 5) - 1 = 0, T r u e (\begin{matrix} x = - 3 i, 鈥� & y = - 5 \end{matrix}) x^{2} + y^{2} = 16 {(- 3 i)}^{2} + {(- 5)}^{2} = 16, T r u e x^{2} - 2 y - 1 = 0 {(- 3 i)}^{2} - 2 (- 5) - 1 = 0, T r u e$

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91影视

In the following exercises, solve the system of equations by using elimination.
$x^{2} + y^{2} = 16 x^{2} - 2 y - 1 = 0$

Short Answer

Step by step solution

Given Information

standard form

Step 3: Substitution method

Check the solution

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=16x2-2y-1=0

Short Answer

Step by step solution

Given Information

standard form

Step 3: Substitution method

Check the solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Discrete Mathematics

Geometry

Logic and Functions

Pure Maths

Decision Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, solve the system of equations by using elimination.
$x^{2} + y^{2} = 16 x^{2} - 2 y - 1 = 0$