Chapter 11: Q. 4 (page 795)

solve each system of equations using the method
of substitution or the method of elimination. If the system has no
solution, say that it is inconsistent.
$\{\begin{cases} 3 x + 2 y - 8 z = - 3 \\ - x - \frac{2}{3} y + z = 1 \\ 6 x - 3 y + 15 z = 8 \end{cases}$

Short Answer

Expert verified

The solution of the given equation is $(\frac{1}{3}, - 2, 0)$

Step by step solution

Step 1. Given

$\{\begin{cases} 3 x + 2 y - 8 z = - 3 \\ - x - \frac{2}{3} y + z = 1 \\ 6 x - 3 y + 15 z = 8 \end{cases}$

Step 2. Calculation

$\{\begin{cases} 3 x + 2 y - 8 z = - 3 . . . . . . (1) \\ - x - \frac{2}{3} y + z = 1 . . . . . . . . . . (2) \\ 6 x - 3 y + 15 z = 8 . . . . . . . . (3) \end{cases} c o n s i d e r e q u a t i o n 2 - 3 x - 2 y + 3 z = 3 A d d e q . 2 w i t h e q . 1 w e g e t - 5 z = 0 z = 0 S u b s t i t u t i n g t h e v a l u e o f z i n e q . 1 a n d e q . 2 w e g e t 3 x + 2 y - 8 (0) = - 3 . . . . . (4) 6 x - 3 y + 15 (0) = 8 . . . . . . . (5) M u l t i p l y 3 w i t h e q . 4 a n d 2 w i t h e q . 5 a n d a d d b o t h 21 x = 7 x = \frac{1}{3} s u b s t i t u t e v a l u e o f x i n e q 4 . 3 (\frac{1}{3}) + 2 y = - 3 y = - 2$

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solve each system of equations using the method
of substitution or the method of elimination. If the system has no
solution, say that it is inconsistent.
$\{\begin{cases} 3 x + 2 y - 8 z = - 3 \\ - x - \frac{2}{3} y + z = 1 \\ 6 x - 3 y + 15 z = 8 \end{cases}$

Short Answer

Step by step solution

Step 1. Given

Step 2. Calculation

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solve each system of equations using the methodof substitution or the method of elimination. If the system has nosolution, say that it is inconsistent.3x+2y-8z=-3-x-23y+z=16x-3y+15z=8

Short Answer

Step by step solution

Step 1. Given

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Mechanics Maths

Probability and Statistics

Decision Maths

Geometry

Applied Mathematics

Study anywhere. Anytime. Across all devices.

solve each system of equations using the method
of substitution or the method of elimination. If the system has no
solution, say that it is inconsistent.
$\{\begin{cases} 3 x + 2 y - 8 z = - 3 \\ - x - \frac{2}{3} y + z = 1 \\ 6 x - 3 y + 15 z = 8 \end{cases}$