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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. 225 (page 1148)

In the following exercise, solve the system of equations by using elimination.
$\{\begin{cases} x^{2} - y^{2} = - 5 \\ 3 x^{2} + 2 y^{2} = 30 \end{cases}$

Short Answer

Expert verified

$(- 2, - 3), (- 2, 3), (2, - 3), (2, 3)$

Step by step solution

01

Step 1. Given information.

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

$\{\begin{cases} x^{2} - y^{2} = - 5 \\ 3 x^{2} + 2 y^{2} = 30 \end{cases}$

02

Step 2. Solving the system of equations.

Here both the equations are in standard form.

To eliminate $y^{2}$ , multiply both sides of the first equation by $2$ and add it with the second equation:

$2 (x^{2} - y^{2}) + (3 x^{2} + 2 y^{2}) = - 5 脳 2 + 30$

Distributing and simplifying

$2 x^{2} - 2 y^{2} + 3 x^{2} + 2 y^{2} = - 10 + 30 5 x^{2} = 20 x^{2} = \frac{20}{5} = 4 x = 卤 \sqrt{4} x = 卤 2$

So, the values of $x$ are $x = 2$ and $x = - 2$ .

Substituting the $x$ values in the first equation:

When $x = 2$ :

${(2)}^{2} - y^{2} = - 5 y^{2} = 5 + 4 = 9 y = 卤 \sqrt{9} y = 卤 3$

When $x = - 2$ :

${(- 2)}^{2} - y^{2} = - 5 y^{2} = 5 + 4 y = 卤 \sqrt{9} y = 卤 3$

Expressing the solutions as ordered pairs:

$(- 2, - 3), (- 2, 3), (2, - 3), (2, 3)$

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Most popular questions from this chapter

In the following exercises, subtract the polynomials.

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