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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. 30 (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.
$\{\begin{cases} \frac{1}{2} x + y = - 2 \\ x - 2 y = 8 \end{cases}$

Short Answer

Expert verified

The solution is $x = 2, y = - 3 and in ordered pair is (2, - 3) .$

Step by step solution

01

Step 1. Given Information

The given system of equation is

$\{\begin{cases} \frac{1}{2} x + y = - 2 \\ x - 2 y = 8 \end{cases}$

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

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

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

03

Step 3. Use Cramer's rule

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

$D_{x} = |\begin{matrix} - 2 & 1 \\ 8 & - 2 \end{matrix}| D_{x} = (- 2) (- 2) - (1) (8) D_{x} = 4 - 8 D_{x} = - 4$

And

$D_{y} = |\begin{matrix} \frac{1}{2} & - 2 \\ 1 & 8 \end{matrix}| D_{y} = (\frac{1}{2}) (8) - (- 2) (1) D_{y} = 4 + 2 D_{y} = 6$

04

Step 4. Finding x and y

By using Cramer's rule, the values of xand yare

$x = \frac{D_{x}}{D} a n d y = \frac{D_{y}}{D} x = \frac{- 4}{- 2} a n d y = \frac{6}{- 2} x = 2 a n d y = - 3$

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Most popular questions from this chapter

The product of two numbers is $4$ , and the sum of their squares is $8$ . Find the numbers.

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

$x - y - z = 1 - x + 2 y - 3 z = - 4 3 x - 2 y - 7 z = 0$

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

$x y = 1; y = 2 x + 1$

Graph each inequality by hand.

$3 x + 2 y 鈮� 6$

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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