Chapter 11: Q. 7 (page 772)

Graph each equation of the system. Then solve the system to find the points of intersection.
$\{\begin{cases} y = \sqrt{36 - x^{2}} \\ y = 8 - x \end{cases}$

Short Answer

Expert verified

Solutions of system of equations $\{\begin{cases} y = \sqrt{36 - x^{2}} \\ y = 8 - x \end{cases}$ are $(4 + \sqrt{2}, 4 - \sqrt{2}) & (4 - \sqrt{2}, 4 + \sqrt{2})$ and the graph is

Step by step solution

Step 1. Given data

The given system of equations is

$\{\begin{cases} y = \sqrt{36 - x^{2}} \dots (i) \\ y = 8 - x \dots (i i) \end{cases}$

Step 2. Graph of the system of equations

Plot the graph of $y = \sqrt{36 - x^{2}} & y = 8 - x$ on same cartesian plane

Step 3. Solution of system

Equate both equations

$\sqrt{36 - x^{2}} = 8 - x 36 - x^{2} = {(8 - x)}^{2} 36 - x^{2} = x^{2} - 16 x + 64 2 x^{2} - 16 x + 28 = 0$

use quadratic formula

$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a} x = \frac{- (- 16) \pm \sqrt{{(- 16)}^{2} - 4 (2) (28)}}{2 (2)} x = \frac{16 \pm \sqrt{32}}{4} x = 4 \pm \sqrt{2}$

Step 4. Solution of system

Substitute $x = 4 + \sqrt{2}$ in equation ii

$y = 8 - x y = 8 - (4 + \sqrt{2}) y = 4 - \sqrt{2}$

Substitute $x = 4 - \sqrt{2}$ in equation ii

$y = 8 - x y = 8 - (4 - \sqrt{2}) y = 4 + \sqrt{2}$

So solutions of the system are $(4 + \sqrt{2}, 4 - \sqrt{2}) & (4 - \sqrt{2}, 4 + \sqrt{2})$

Step 6. Point of intersection

Locate $(4 + \sqrt{2}, 4 - \sqrt{2}) & (4 - \sqrt{2}, 4 + \sqrt{2})$ for point of interception in the graph of a system of equations

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Graph each equation of the system. Then solve the system to find the points of intersection.
$\{\begin{cases} y = \sqrt{36 - x^{2}} \\ y = 8 - x \end{cases}$

Short Answer

Step by step solution

Step 1. Given data

Step 2. Graph of the system of equations

Step 3. Solution of system

Step 4. Solution of system

Step 6. Point of intersection

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Graph each equation of the system. Then solve the system to find the points of intersection.y=36-x2y=8-x

Short Answer

Step by step solution

Step 1. Given data

Step 2. Graph of the system of equations

Step 3. Solution of system

Step 4. Solution of system

Step 6. Point of intersection

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Theoretical and Mathematical Physics

Mechanics Maths

Logic and Functions

Discrete Mathematics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Graph each equation of the system. Then solve the system to find the points of intersection.
$\{\begin{cases} y = \sqrt{36 - x^{2}} \\ y = 8 - x \end{cases}$