Chapter 11: Q. 320 (page 1159)

In the following exercises, solve the system of equations by using elimination.
$x^{2} - y^{2} = 5 - 2 x^{2} - 3 y^{2} = - 30$

Short Answer

Expert verified

Solution

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

Step by step solution

Given Information

Given equations are

$x^{2} - y^{2} = 5 - 2 x^{2} - 3 y^{2} = - 30$

Eliminate a variable 'x'

$x^{2} - y^{2} = 5 - 2 x^{2} - 3 y^{2} = - 30 M u l t i p l y t h e f i r s t e q u a t i o n b y 2 2 x^{2} - 2 y^{2} = 10 - 2 x^{2} - 3 y^{2} = - 30 - - - - - - - - - - - - - - 5 y^{2} = - 20 y^{2} = 4 y = \pm 2$

solve for x

we got y= +2, y=-2

Substitute it in any one of the equation and solve for x

$x^{2} - y^{2} = 5 y = + 2 x^{2} - 2^{2} = 5 x^{2} - 4 = 5 x^{2} = 9 x = \pm 3 (2, 3) a n d (2, - 3) x^{2} - y^{2} = 5 y = - 2 x^{2} - {(- 2)}^{2} = 5 x^{2} - 4 = 5 x^{2} = 9 x = \pm 3 (- 2, 3) a n d (- 2, - 3)$

verify the solution

$(3, 2) x^{2} - y^{2} = 5 {(3)}^{2} - {(2)}^{2} = 5, T r u e - 2 x^{2} - 3 y^{2} = - 30 - 2 {(3)}^{2} - 3 {(2)}^{2} = - 30, t r u e (- 3, 2) x^{2} - y^{2} = 5 {(- 3)}^{2} - {(2)}^{2} = 5, T r u e - 2 x^{2} - 3 y^{2} = - 30 - 2 {(- 3)}^{2} - 3 {(2)}^{2} = - 30, t r u e (3, - 2) x^{2} - y^{2} = 5 {(3)}^{2} - {(- 2)}^{2} = 5, T r u e - 2 x^{2} - 3 y^{2} = - 30 - 2 {(3)}^{2} - 3 {(- 2)}^{2} = - 30, t r u e (- 3, - 2) x^{2} - y^{2} = 5 {(- 3)}^{2} - {(- 2)}^{2} = 5, T r u e - 2 x^{2} - 3 y^{2} = - 30 - 2 {(- 3)}^{2} - 3 {(- 2)}^{2} = - 30, t r u e$

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In the following exercises, solve the system of equations by using elimination.
$x^{2} - y^{2} = 5 - 2 x^{2} - 3 y^{2} = - 30$

Short Answer

Step by step solution

Given Information

Eliminate a variable 'x'

solve for x

verify the solution

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In the following exercises, solve the system of equations by using elimination.x2-y2=5-2x2-3y2=-30

Short Answer

Step by step solution

Given Information

Eliminate a variable 'x'

solve for x

verify the solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Logic and Functions

Calculus

Pure Maths

Theoretical and Mathematical Physics

Geometry

Study anywhere. Anytime. Across all devices.

In the following exercises, solve the system of equations by using elimination.
$x^{2} - y^{2} = 5 - 2 x^{2} - 3 y^{2} = - 30$