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" $y^{2} + y + x^{2} - x - 2 = 0 y^{2} + y + {(\frac{1}{2})}^{2} + x^{2} - x + {(\frac{1}{2})}^{2} = 2 + {(\frac{1}{2})}^{2} + {(\frac{1}{2})}^{2} {(y + \frac{1}{2})}^{2} + {(x - \frac{1}{2})}^{2} = 2 + \frac{1}{2} {(y + \frac{1}{2})}^{2} + {(x - \frac{1}{2})}^{2} = \frac{5}{2} {(y + \frac{1}{2})}^{2} = - {(x - \frac{1}{2})}^{2} + \frac{5}{2} y + \frac{1}{2} = \pm \sqrt{- {(x - \frac{1}{2})}^{2} + \frac{5}{2}} y = \pm \sqrt{- {(x - \frac{1}{2})}^{2} + \frac{5}{2}} - \frac{1}{2}$

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

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

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

From the second equation, we can see that $x \neq 0$ . 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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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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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

Probability and Statistics

Calculus

Theoretical and Mathematical Physics

Pure Maths

Logic and Functions

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Graph the equations given in Problem $49$ .