Q. 80 - Precalculus Enhanced with Graphing Utilities | StudyQuestionHub

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Q. 80

Question

In Problems 75– 82, algebraically solve each system of equations using any method you wish.

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

Step-by-Step Solution

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Answer

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

1Step 1. Given information

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

2Step 2. Finding the values of x , y   a n d   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

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

$- x + 0 y - 13 z = 16 \dots \dots \dots (1)$

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

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

$2 x + 0 y + 26 z = - 14 \dots \dots \dots (2)$

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

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

$0 x + 0 y = 46 \dots \dots \dots \dots (3)$

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

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