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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. 223 (page 1148)

In the following exercise, solve the system of equations by using elimination.
$\{\begin{cases} x^{2} - y^{2} = 3 \\ 2 x^{2} + y^{2} = 6 \end{cases}$

Short Answer

Expert verified

$(\sqrt{3}, 0)$ and $(- \sqrt{3}, 0)$

Step by step solution

01

Step 1. Given information.

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

$\{\begin{cases} x^{2} - y^{2} = 3 \\ 2 x^{2} + y^{2} = 6 \end{cases}$

02

Step 2. Solving by elimination.

By adding the two equations, we get the following:

$3 x^{2} = 9$

Simplifying

$x^{2} = \frac{9}{3} = 3 x = 卤 \sqrt{3}$

Substituting the values of $x$ into the first equation:

When $x = \sqrt{3}$ :

${(\sqrt{3})}^{2} - y^{2} = 3 y^{2} = 3 - 3 = 0 y = 0$

When $x = - \sqrt{3}$ :

${(- \sqrt{3})}^{2} - y^{2} = 3 y^{2} = 3 - 3 = 0 y = 0$

Expressing the solution as ordered pairs:

$(\sqrt{3}, 0)$ and $(- \sqrt{3}, 0)$

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