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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. 80 (page 757)

In Problems 75鈥� 82, algebraically solve each system of equations using any method you wish.
$\{\begin{cases} 3 x + 2 y - z = 2 \\ 2 x + y + 6 z = - 7 \\ 2 x + 2 y - 14 z = 17 \end{cases}$

Short Answer

Expert verified

The given equations $\{\begin{cases} 3 x + 2 y - z = 2 \\ 2 x + y + 6 z = - 7 \\ 2 x + 2 y - 14 z = 17 \end{cases}$ has no solution.Hence the system is inconsistent

Step by step solution

01

Step 1. Given information

The given equations $\{\begin{cases} 3 x + 2 y - z = 2 \\ 2 x + y + 6 z = - 7 \\ 2 x + 2 y - 14 z = 17 \end{cases}$

02

Step 2. Finding the values of x,y and z

Consider the equations $3 x + 2 y - z = 2, 2 x + y + 6 z = - 7$ and $2 x + 2 y - 14 z = 17$ .To solve these equations,it seems easiest to eliminate the variable y first.So,we multiply the second equation bt 2 and the substract it from first equation

$- 3 x + 2 y - 1 z = 2 4 x + 2 y + 12 z = - 14 - x + 0 y - 13 z = 16$

$- x + 0 y - 13 z = 16 鈰� 鈰� 鈰� (1)$

Again we multiplay the second equation by 2 and the substract last equation from it

$- 4 x + 2 y + 12 z = - 14 2 x + 2 y - 14 z = 17 2 x + 0 y + 26 z = - 14$

$2 x + 0 y + 26 z = - 14 鈰� 鈰� 鈰� (2)$

Now we multiplay equation (1) by -2 and then substract equation (2)

$- 2 x + 26 y = 32 2 x + 26 y = - 14 0 x + 0 y = 46$

$0 x + 0 y = 46 鈰� 鈰� 鈰� 鈰� (3)$

Equation (3) has no solution.Hence the system is inconsistent

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Most popular questions from this chapter

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

$\{\begin{matrix} 2 x + \frac{1}{2} y = 0 \\ 3 x - 4 y = - \frac{19}{2} \end{matrix} x = - \frac{1}{2}, y = 2; (- \frac{1}{2}, 2)$

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

$y = 3 x - 5; x^{2} + y^{2} = 5$

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$y 鈮� x^{2} - 1$

If a system of equations has no solution, it is said to be _______.

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