Chapter 11: Q. 318 (page 1069)

In the following exercises, solve the system of equations by using substitution.
$x^{2} + 4 y^{2} = 4 2 x - y = 1$

Short Answer

Expert verified

$S o l u t i o n : \begin{matrix} x = \frac{16}{17}, & y = \frac{15}{17} \end{matrix} \begin{matrix} x = 0, & y = - 1 \end{matrix}$

Step by step solution

Given Information

Two equations are

$x^{2} + 4 y^{2} = 4 2 x - y = 1$

Identify the graph and check the possible solution

The graph of two equations

Both the graph intersects at

(0,-1) and (0.941, 0.882)

Solve the second equation for y

$2 x - y = 1 2 x - 1 = y y = 2 x - 1$

Substitute it in first equation and solve for x

$x^{2} + 4 {(2 x - 1)}^{2} = 4 17 x^{2} - 16 x + 4 = 4 17 x^{2} - 16 x = 0 x (17 x - 16) = 0 x = 0 17 x - 16 = 0 17 x = 16 x = \frac{16}{17}$

Solve for y

Substitute the x value and find out y

$y = 2 x - 1 x = 0 y = 2 (0) - 1 y = - 1 x = \frac{16}{17} y = 2 (\frac{16}{17}) - 1 y = \frac{15}{17}$

Solution is

$(0, - 1) (\frac{16}{17}, \frac{15}{17})$

Check the solution

Substitute each ordered pair and verify the solution

$(0, - 1) 2 x - y = 1 2 (0) - (- 1) = 1, T r u e x^{2} + 4 y^{2} = 4 {(0)}^{2} + 4 {(- 1)}^{2} = 4, T r u e (\frac{16}{17}, \frac{15}{17}) 2 x - y = 1 2 (\frac{16}{17}) - (\frac{15}{17}) = 1, T r u e x^{2} + 4 y^{2} = 4 {(\frac{16}{17})}^{2} + 4 {(\frac{15}{17})}^{2} = 4, T r u e$

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In the following exercises, solve the system of equations by using substitution.
$x^{2} + 4 y^{2} = 4 2 x - y = 1$

Short Answer

Step by step solution

Given Information

Identify the graph and check the possible solution

Solve the second equation for y

Solve for y

Check the solution

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In the following exercises, solve the system of equations by using substitution.x2+4y2=42x-y=1

Short Answer

Step by step solution

Given Information

Identify the graph and check the possible solution

Solve the second equation for y

Solve for y

Check the solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Probability and Statistics

Theoretical and Mathematical Physics

Applied Mathematics

Calculus

Logic and Functions

Study anywhere. Anytime. Across all devices.

In the following exercises, solve the system of equations by using substitution.
$x^{2} + 4 y^{2} = 4 2 x - y = 1$