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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. 221 (page 1148)

In the following exercise, solve the system of equations by using elimination:
$\{\begin{cases} x^{2} + y^{2} = 16 \\ x^{2} - y^{2} = 16 \end{cases}$

Short Answer

Expert verified

$(4, 0)$ and $(- 4, 0)$

Step by step solution

01

Step 1. Given information.

In this case, the following system of equations is given:

$\{\begin{cases} x^{2} + y^{2} = 16 \\ x^{2} - y^{2} = 16 \end{cases}$

02

Step 2. Solution by the method of elimination.

Both equations are in standard form.

Adding the two equations gives

$2 x^{2} = 32$

Simplify:

$x^{2} = \frac{32}{2} = 16 x = 卤 \sqrt{16} x = + 4 or - 4$

Substitute the values of $x$ into one of the original equations and solve for $y$ :

When $x = 4$ :

$4^{2} + y^{2} = 16$

Simplifying:

$y^{2} = 16 - 4^{2} = 0 y = 0$

When $x = - 4$ :

${(- 4)}^{2} + y^{2} = 16 y^{2} = 16 - 16 = 0 y = 0$

Write each solution as ordered pair:

$(4, 0)$ and $(- 4, 0)$

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