Q. 44 Solve the system. Use any method... [FREE SOLUTION]

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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 11: Q. 44 (page 773)

Solve the system. Use any method you wish.
$\{\begin{cases} \frac{2}{x^{2}} - \frac{3}{y^{2}} + 1 = 0 \\ \frac{6}{x^{2}} - \frac{7}{y^{2}} + 2 = 0 \end{cases}$

Short Answer

Expert verified

The solution of system of equations are $(2, - \sqrt{2}), (2, \sqrt{2}), (- 2, - \sqrt{2}), (- 2, \sqrt{2})$ .

Step by step solution

Step 1. Given information.

Consider the given question,

$\{\begin{cases} \frac{2}{x^{2}} - \frac{3}{y^{2}} + 1 = 0 . . . . . . (i) \\ \frac{6}{x^{2}} - \frac{7}{y^{2}} + 2 = 0 . . . . . . . (i i) \end{cases}$

Multiply equation (i) by $x^{2} y^{2}$ ,

$\frac{2 x^{2} y^{2}}{x^{2}} - \frac{3 x^{2} y^{2}}{y^{2}} + x^{2} y^{2} = 0 2 y^{2} - 3 x^{2} + x^{2} y^{2} = 0 . . . . . . (i i i)$

Multiply equation (ii) by $x^{2} y^{2}$ ,

$\frac{6 x^{2} y^{2}}{x^{2}} - \frac{7 x^{2} y^{2}}{y^{2}} + 2 x^{2} y^{2} = 0 6 y^{2} - 7 x^{2} + 2 x^{2} y^{2} = 0 . . . . . . (i v)$

Step 2. Multiply equation (iii) by 3.

Multiply equation (iii) by $3$ ,

$6 y^{2} - 9 x^{2} + 3 x^{2} y^{2} = 0 . . . . . . (v)$

Subtract equation (v) and (iv),

$(6 y^{2} - 9 x^{2} + 3 x^{2} y^{2}) - (6 y^{2} - 7 x^{2} + 2 x^{2} y^{2}) = 0 6 y^{2} - 9 x^{2} + 3 x^{2} y^{2} - 6 y^{2} + 7 x^{2} - 2 x^{2} y^{2} = 0 2 x^{2} = x^{2} y^{2} y = - \sqrt{2}, \sqrt{2}$

Step 3. Substitute the values of y in equation (iv).

Substitute $y = \sqrt{2}$ in equation (iv),

$6 {(\sqrt{2})}^{2} - 7 x^{2} + 2 x^{2} {(\sqrt{2})}^{2} = 0 12 - 7 x^{2} + 4 x^{2} = 0 12 = 3 x^{2} x = 2, - 2$

Substitute $y = - \sqrt{2}$ in equation (iv),

$6 {(- \sqrt{2})}^{2} - 7 x^{2} + 2 x^{2} {(- \sqrt{2})}^{2} = 0 12 - 7 x^{2} + 4 x^{2} = 0 12 = 3 x^{2} x = 2, - 2$

Therefore, the solution sets are $(2, - \sqrt{2}), (2, \sqrt{2}), (- 2, - \sqrt{2}), (- 2, \sqrt{2})$ .

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91影视

Solve the system. Use any method you wish.
$\{\begin{cases} \frac{2}{x^{2}} - \frac{3}{y^{2}} + 1 = 0 \\ \frac{6}{x^{2}} - \frac{7}{y^{2}} + 2 = 0 \end{cases}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Multiply equation (iii) by 3.

Step 3. Substitute the values of y in equation (iv).

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91影视

Solve the system. Use any method you wish.2x2-3y2+1=06x2-7y2+2=0

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Multiply equation (iii) by 3.

Step 3. Substitute the values of y in equation (iv).

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

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Study anywhere. Anytime. Across all devices.

Solve the system. Use any method you wish.
$\{\begin{cases} \frac{2}{x^{2}} - \frac{3}{y^{2}} + 1 = 0 \\ \frac{6}{x^{2}} - \frac{7}{y^{2}} + 2 = 0 \end{cases}$