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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 11: Q. 43 (page 794)

In Problems 39鈥�43, solve each system of equations.
$\{\begin{cases} x^{2} - 3 x + y^{2} + y = - 2 \\ \frac{x^{2} - x}{y} + y + 1 = 0 \end{cases}$

Short Answer

Expert verified

Solutions of the system of equations $\{\begin{cases} x^{2} - 3 x + y^{2} + y = - 2 \\ \frac{x^{2} - x}{y} + y + 1 = 0 \end{cases}$ are

Step by step solution

01

Step 1. Given data

The given system of equation is

$\{\begin{cases} x^{2} - 3 x + y^{2} + y = - 2 \\ \frac{x^{2} - x}{y} + y + 1 = 0 \end{cases}$

02

Step 2. Formation of the single-variable equation

Multiply y to both sides of the equation $\frac{x^{2} - x}{y} + y + 1 = 0$

role="math" localid="1646951235780" $y (\frac{x^{2} - x}{y} + y + 1) = y (0) x^{2} - x + y^{2} + y = 0$

so the new system of equation isrole="math" localid="1646951485440" $\{\begin{cases} x^{2} - 3 x + y^{2} + y = - 2 鈰� i \\ x^{2} - x + y^{2} + y = 0 鈰� i i \end{cases}$

03

Step 3. Formation of the single-variable equation

Subtract equation ii from equation i

$(x^{2} - 3 x + y^{2} + y) - (x^{2} - x + y^{2} + y) = - 2 - 0 - 2 x = - 2 x = 1$

04

Step 4. Solution of the system of equations

Substitute $x = 1$ in equation $x^{2} - 3 x + y^{2} + y = - 2$

$x^{2} - 3 x + y^{2} + y = - 2 1^{2} - 3 (1) + y^{2} + y = - 2 y^{2} + y = 0 y (y + 1) = 0$

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Most popular questions from this chapter

Graph each inequality by hand.

$x^{2} + y^{2} > 1$

The altitude of an isosceles triangle drawn to its base is $3 c m$ , and its perimeter is $18 c m$ . Find the length of its base.

The sum of two numbers is the same as their product, and the difference of their reciprocals is $3$ . Find the numbers.

solve each system of equations. If the system has no solution, say that it is inconsistent.

$x - y = 6 2 x - 3 z = 16 2 y + z = 4$

Solve each system of equations. If the system has no solution, say that it is inconsistent.

$\{\begin{matrix} x + 2 y = 4 \\ 2 x + 4 y = 8 \end{matrix}$

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