Chapter 11: Q. 321 (page 1159)

In the following exercises, solve the system of equations by using elimination.
$4 x^{2} + 9 y^{2} = 36 3 y^{2} - 4 x = 12$

Short Answer

Expert verified

Solution for the system of equation

$\begin{matrix} x = 0, & y = 2 \end{matrix} (0, 2) \begin{matrix} x = 0, & y = - 2 \end{matrix} (0, - 2) \begin{matrix} x = - 3, & y = 0 \end{matrix} (- 3, 0)$

Step by step solution

Given information

Two given equations are

$4 x^{2} + 9 y^{2} = 36 3 y^{2} - 4 x = 12$

Eliminate x or y

$4 x^{2} + 9 y^{2} = 36 3 y^{2} - 4 x = 12 M u l t i p l y t h e s e c o n d e q u a t i o n b y - 3 4 x^{2} + 9 y^{2} = 36 - 9 y^{2} + 12 x = - 36 - - - - - - - - - - - - 4 x^{2} + 12 x = 0 4 x (x + 3) = 0 4 x = 0, x = 0 x + 3 = 0 x = - 3$

Solve for y

Substitute the value of x and solve for x

$3 y^{2} - 4 x = 12 x = 0 3 y^{2} - 4 (0) = 12 3 y^{2} = 12 y^{2} = 4 y = \pm 2 x = - 3 3 y^{2} - 4 (- 3) = 12 3 y^{2} = 0 y^{2} = 0 y = 0$

verify solution

Solution is

$\begin{matrix} x = 0, & y = 2 \end{matrix} 4 {(0)}^{2} + 9 {(2)}^{2} = 36, T r u e 3 {(2)}^{2} - 4 (0) = 12, t r u e \begin{matrix} x = 0, & y = - 2 \end{matrix} 4 {(0)}^{2} + 9 {(- 2)}^{2} = 36, T r u e 3 {(- 2)}^{2} - 4 (0) = 12, t r u e \begin{matrix} x = - 3, & y = 0 \end{matrix} 4 {(- 3)}^{2} + 9 {(0)}^{2} = 36, T r u e 3 {(0)}^{2} - 4 (- 3) = 12, t r u e$

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In the following exercises, solve the system of equations by using elimination.
$4 x^{2} + 9 y^{2} = 36 3 y^{2} - 4 x = 12$

Short Answer

Step by step solution

Given information

Eliminate x or y

Solve for y

verify solution

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In the following exercises, solve the system of equations by using elimination.4x2+9y2=363y2-4x=12

Short Answer

Step by step solution

Given information

Eliminate x or y

Solve for y

verify solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Discrete Mathematics

Probability and Statistics

Logic and Functions

Statistics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, solve the system of equations by using elimination.
$4 x^{2} + 9 y^{2} = 36 3 y^{2} - 4 x = 12$