Chapter 11: Q. 317 (page 1159)

In the following exercises, solve the system of equations by using substitution.
$9 x^{2} + 4 y^{2} = 36 y - x = 5$

Short Answer

Expert verified

Solution

$\begin{matrix} x = - \frac{20}{13} + i \frac{12 \sqrt{3}}{13}, & y = \frac{45}{13} + i \frac{12 \sqrt{3}}{13} \end{matrix} \begin{matrix} x = - \frac{20}{13} - i \frac{12 \sqrt{3}}{13}, & y = \frac{45}{13} - i \frac{12 \sqrt{3}}{13} \end{matrix}$

Step by step solution

Given Information

System of equations

$9 x^{2} + 4 y^{2} = 36 y - x = 5$

Substitute y equation

$9 x^{2} + 4 y^{2} = 36 y - x = 5 y = 5 + x s u b s i t u t e i t i n f i r s t e q u a t i o n 9 x^{2} + 4 {(5 + x)}^{2} = 36 9 x^{2} + 4 (x^{2} + 10 x + 25) = 36 9 x^{2} + 4 x^{2} + 40 x + 100 = 36 13 x^{2} + 40 x + 64 = 0 A p p l y q u a d r a t i c f o r m u l a x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a} x = \frac{- 40 \pm \sqrt{40^{2} - 4 (13) (64)}}{2 (13)} x = \frac{- 40 \pm 24 \sqrt{3} i}{2 \cdot 13} x = - \frac{20}{13} - i \frac{12 \sqrt{3}}{13} x = - \frac{20}{13} + i \frac{12 \sqrt{3}}{13}$

Substitute x and find out y

$y = x + 5 x = - \frac{20}{13} + i \frac{12 \sqrt{3}}{13} y = - \frac{20}{13} + i \frac{12 \sqrt{3}}{13} + 5 y = y = \frac{45}{13} + i \frac{12 \sqrt{3}}{13} x = - \frac{20}{13} - i \frac{12 \sqrt{3}}{13} y = - \frac{20}{13} - i \frac{12 \sqrt{3}}{13} + 5 y = \frac{45}{13} - i \frac{12 \sqrt{3}}{13}$

Solution

solution for the system of equations

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In the following exercises, solve the system of equations by using substitution.
$9 x^{2} + 4 y^{2} = 36 y - x = 5$

Short Answer

Step by step solution

Given Information

Substitute y equation

Substitute x and find out y

Solution

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In the following exercises, solve the system of equations by using substitution.9x2+4y2=36y-x=5

Short Answer

Step by step solution

Given Information

Substitute y equation

Substitute x and find out y

Solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Applied Mathematics

Discrete Mathematics

Decision Maths

Geometry

Probability and Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises, solve the system of equations by using substitution.
$9 x^{2} + 4 y^{2} = 36 y - x = 5$