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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. 224 (page 1148)

In the following exercise, solve the system of equations by using elimination.
$\{\begin{cases} 4 x^{2} - y^{2} = 4 \\ 4 x^{2} + y^{2} = 4 \end{cases}$

Short Answer

Expert verified

$(1, 0)$ , $(- 1, 0)$

Step by step solution

01

Step 1. Given information.

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

$\{\begin{cases} 4 x^{2} - y^{2} = 4 \\ 4 x^{2} + y^{2} = 4 \end{cases}$

02

Step 2. Solving the system of equations.

Adding the two equations:

$8 x^{2} = 8$

Simplifying

$x^{2} = \frac{8}{8} x = 卤 1$

Substituting the values of $x$ into any one of the two equations:

When $x = 1$ :

$4 (1^{2}) - y^{2} = 4 y^{2} = 4 - 4 = 0 y = 0$

When $x = - 1$ :

$4 {(- 1)}^{2} - y^{2} = 4 y^{2} = 4 - 4 = 0 y = 0$

Expressing the solutions as ordered pairs:

$(1, 0), (- 1, 0)$

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Most popular questions from this chapter

Simplify a Complex Rational Expression by Using the LCD.

In the following exercises, simplify each complex rational expression by using the LCD. $\frac{\frac{3}{s + 6} + \frac{5}{s - 6}}{\frac{1}{s^{2} - 36} + \frac{4}{s + 6}}$

Solve $(4 p + 3) (4 p - 3) = 0$

Simplify the complex rational expression by writing it as division:

$\frac{\frac{1}{a} + \frac{1}{b}}{\frac{1}{a^{2}} - \frac{1}{b^{2}}}$

Factor completely, $5 x^{3} + 15 x^{2} - 20 x$

Use the Zero Product Property in the following exercises to solve.

$(a - 3) (a + 7) = 0$

See all solutions

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