Chapter 11: Q. 29 (page 773)

Graph each equation of the system. Then solve the system to find the points of intersection.
$\{\begin{cases} x + y + 1 = 0 \\ x^{2} + y^{2} + 6 y - x = - 5 \end{cases}$

Short Answer

Expert verified

The point of intersection is $(0, - 1) & (\frac{5}{2}, - \frac{7}{2})$ .

Step by step solution

Step 1. Given information

$\{\begin{cases} x + y + 1 = 0 \\ x^{2} + y^{2} + 6 y - x = - 5 \end{cases}$

Step 2. Graphing each equation

$x + y + 1 = 0$

$x^{2} + y^{2} + 6 y - x = - 5$

Step 3. Calculation of intersection point

$C o n s i d e r, x + y + 1 = 0 . . . . . (1) x^{2} + y^{2} + 6 y - x = - 5 . . . . . (2) N o w s u b s t i t u t i n g t h e v a l u e o f y f r o m e q . 1 i n t o e q . 2 w e g e t x^{2} + {(- x - 1)}^{2} + 6 (- x - 1) - x = - 5 x^{2} + x^{2} + 1 + 2 x - 6 x - 6 - x = - 5 x = 0, \frac{5}{2} N o w s u b s t i t u t i n g v a l u e o f x i n e q . 1 w e g e t y = - 1 y = - \frac{7}{2}$

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Graph each equation of the system. Then solve the system to find the points of intersection.
$\{\begin{cases} x + y + 1 = 0 \\ x^{2} + y^{2} + 6 y - x = - 5 \end{cases}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Graphing each equation

Step 3. Calculation of intersection point

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Graph each equation of the system. Then solve the system to find the points of intersection.x+y+1=0x2+y2+6y-x=-5

Short Answer

Step by step solution

Step 1. Given information

Step 2. Graphing each equation

Step 3. Calculation of intersection point

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Theoretical and Mathematical Physics

Geometry

Logic and Functions

Discrete Mathematics

Decision Maths

Study anywhere. Anytime. Across all devices.

Graph each equation of the system. Then solve the system to find the points of intersection.
$\{\begin{cases} x + y + 1 = 0 \\ x^{2} + y^{2} + 6 y - x = - 5 \end{cases}$