Q. 56 Graph the equations given in Pro... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 11: Q. 56 (page 773)

Graph the equations given in Problem $49$ .

Short Answer

Expert verified

The solution for the graph $\{\begin{cases} y^{2} + y + x^{2} - x - 2 = 0 \\ y + 1 + \frac{x - 2}{y} = 0 \end{cases}$ is,

Step by step solution

Step 1 The equations in problem 49 is,

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

Consider the first equation and solve it for $y$ .

role="math" localid="1647067739485" $y^{2} + y + x^{2} - x - 2 = 0 y^{2} + y + {(\frac{1}{2})}^{2} + x^{2} - x + {(\frac{1}{2})}^{2} = 2 + {(\frac{1}{2})}^{2} + {(\frac{1}{2})}^{2} {(y + \frac{1}{2})}^{2} + {(x - \frac{1}{2})}^{2} = 2 + \frac{1}{2} {(y + \frac{1}{2})}^{2} + {(x - \frac{1}{2})}^{2} = \frac{5}{2} {(y + \frac{1}{2})}^{2} = - {(x - \frac{1}{2})}^{2} + \frac{5}{2} y + \frac{1}{2} = 卤 \sqrt{- {(x - \frac{1}{2})}^{2} + \frac{5}{2}} y = 卤 \sqrt{- {(x - \frac{1}{2})}^{2} + \frac{5}{2}} - \frac{1}{2}$

Step 2 Now consider the second equation and solve it for y.

$y + 1 + \frac{x - 2}{y} = 0 y^{2} + y + x - 2 = 0 y^{2} + y + {(\frac{1}{2})}^{2} = - x + 2 + {(\frac{1}{2})}^{2} {(y + \frac{1}{2})}^{2} = - x + 2 + \frac{1}{4} {(y + \frac{1}{2})}^{2} = - x + \frac{9}{4} y + \frac{1}{2} = 卤 \sqrt{- x + \frac{9}{4}} y = 卤 \sqrt{- x + \frac{9}{4}} - \frac{1}{2}$

Step 3 Now sketch a graph by using the given equations.

From the second equation, we can see that $x 鈮� 0$ . So, the graph has a hole at the points $(0, 1)$ and $(0, - 2)$ . The value $x = 0$ is extraneous and we discard it.

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91影视

Graph the equations given in Problem $49$ .

Short Answer

Step by step solution

Step 1 The equations in problem 49 is,

Step 2 Now consider the second equation and solve it for y.

Step 3 Now sketch a graph by using the given equations.

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91影视

Graph the equations given in Problem 49.

Short Answer

Step by step solution

Step 1 The equations in problem 49 is,

Step 2 Now consider the second equation and solve it for y.

Step 3 Now sketch a graph by using the given equations.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Decision Maths

Geometry

Theoretical and Mathematical Physics

Calculus

Logic and Functions

Study anywhere. Anytime. Across all devices.

Graph the equations given in Problem $49$ .