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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. 16 (page 740)

In Problems 15 鈥� 42, solve each system of equations using Cramer鈥檚 Rule if it is applicable. If Cramer鈥檚 Rule is not applicable, say so.
$\{\begin{cases} x + 2 y = 5 \\ x - y = 3 \end{cases}$

Short Answer

Expert verified

The solution is $x = \frac{11}{3}, y = \frac{2}{3} and in ordered pair is (\frac{11}{3}, \frac{2}{3}) .$

Step by step solution

01

Step 1. Given Information

The given system of equation is

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

We have to solve the system of equations using Cramer's rule if it is applicable.

02

Step 2. Finding the determinant

The determinant D of the coefficients of the variables is

$D = |\begin{matrix} 1 & 2 \\ 1 & - 1 \end{matrix}| D = (1) (- 1) - (2) (1) D = - 1 - 2 D = - 3$

Since $D 鈮� 0$ Cramer's rule is applicable.

03

Step 3. Use Cramer's rule

Let's find $D_{x} and D_{y}$

$D_{x} = |\begin{matrix} 5 & 2 \\ 3 & - 1 \end{matrix}| D_{x} = (5) (- 1) - (2) (3) D_{x} = - 5 - 6 D_{x} = - 11$

And

$D_{y} = |\begin{matrix} 1 & 5 \\ 1 & 3 \end{matrix}| D_{y} = (1) (3) - (5) (1) D_{y} = 3 - 5 D_{y} = - 2$

04

Step 4. Finding x and y

By using Cramer's rule, the values of xandyare

$x = \frac{D_{x}}{D} a n d y = \frac{D_{y}}{D} x = \frac{- 11}{- 3} a n d y = \frac{- 2}{- 3} x = \frac{11}{3} a n d y = \frac{2}{3}$

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Most popular questions from this chapter

The Tortoise and the Hare: In a 21-meter race between a tortoise and a hare, the tortoise leaves 9 minutes before the hare. The hare, by running at an average speed of 0.5 meter per hour faster than the tortoise, crosses the finish line 3minutes before the tortoise. What are the average speeds of the tortoise and the hare?

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

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

In Problems 5鈥�24, graph each equation of the system. Then solve the system to find the points of intersection.

$x^{2} + y^{2} = 4; x^{2} + 2 x + y^{2} = 0$

An area of $52 f e e t^{2}$ is to be enclosed by two squares whose sides are in the ratio of $2 : 3$ . Find the sides of the squares.

In Problems 5鈥�24, graph each equation of the system. Then solve the system to find the points of intersection.

$y = \sqrt{4 - x^{2}}; y = 2 x + 4$

See all solutions

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