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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. 31 (page 773)

Graph each equation of the system. Then solve the system to find the points of intersection.
$\{\begin{cases} 4 x^{2} - 3 x y + 9 y^{2} = 15 \\ 2 x + 3 y = 5 \end{cases}$

Short Answer

Expert verified

The point of intersection is $(2, \frac{1}{3}) & (\frac{1}{2}, \frac{4}{3})$ .

Step by step solution

01

Step 1. Given information

$\{\begin{cases} 4 x^{2} - 3 x y + 9 y^{2} = 15 \\ 2 x + 3 y = 5 \end{cases}$

02

Step 2. Graphing each equation

$4 x^{2} - 3 x y + 9 y^{2} = 15$

$2 x + 3 y = 5$

03

Step 3. Calculation of intersection point

$C o n s i d e r, 4 x^{2} - 3 x y + 9 y^{2} = 15 . . . . . (1) 2 x + 3 y = 5 . . . . . (2) N o w s u b s t i t u t i n g t h e v a l u e o f y f r o m e q . 2 i n t o e q . 1 w e g e t 4 x^{2} - 3 x (\frac{5 - 2 x}{3}) + 9 {(\frac{5 - 2 x}{3})}^{2} = 15 x = (2, \frac{1}{2}) N o w s u b s t i t u t i n g v a l u e o f x i n e q . 2 w e g e t 2 x + 3 y = 5 y = (\frac{1}{3}, \frac{4}{3})$

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Most popular questions from this chapter

In Problems 23鈥�34, graph each system of linear inequalities by hand. Verify your results using a graphing utility

$\{\begin{array}{r} x - 2 y 鈮� 6 \\ 2 x - 4 y 鈮� 0 \end{array}$

The ratio of a to b is $\frac{2}{3}$ . The sum of a and b is $10$ . What is the ratio of $a + b$ to $b - a$ ?

Verify that the values of the variables listed are solutions of the system of equations.

$\{\begin{matrix} \begin{array}{rcl} 4 x - 5 z & = & 6 \\ 5 y - z & = & - 17 \end{array} \\ - x - 6 y + 5 z = 24 \end{matrix} x = 4, y = - 3, z = 2; (4, - 3, 2)$

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

$\{\begin{cases} 2 x + 4 y = \frac{2}{3} \\ 3 x - 5 y = - 1 \end{cases}$

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

$\{\begin{matrix} 4 x + 5 y = - 3 \\ - 2 y = - 8 \end{matrix}$

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