Chapter 11: Q. 81 (page 757)

In Problems 75– 82, algebraically solve each system of equations using any method you wish.
$\{\begin{cases} 2 x - 3 y + z = 4 \\ - 3 x + 2 y - z = 17 \\ - 5 y + z = 6 \end{cases}$

Short Answer

Expert verified

The given equations $\{\begin{cases} 2 x - 3 y + z = 4 \\ - 3 x + 2 y - z = 17 \\ - 5 y + z = 6 \end{cases}$ has no solution.Hence the system is inconsistent

Step by step solution

Step 1. Given information

The given equations $\{\begin{cases} 2 x - 3 y + z = 4 \\ - 3 x + 2 y - z = 17 \\ - 5 y + z = 6 \end{cases}$

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

Consider the equations $2 x - 3 y + z = 4, - 3 x + 2 y - z = 17$ and $- 5 y + z = 6$ .To solve these equations,it seems easiest to eliminate the variable z first.So,we add the first two equations

$2 x - 3 y + z = 4 + - 3 x + 2 y - z = 17 - x - y = 21$

$- x - y = 21 \dots \dots \dots \dots (1)$

Again we add the last two equations

$- 3 x + 2 y - z = 17 + - 5 y + z = 6 - 3 x - 3 y = 23$

$- 3 x - 3 y = 23 \dots \dots (2)$

Now we multiplay equation (1) by 3 and then substract equation (2) from it

$- 3 x - 3 y = 63 - 3 x - 3 y = 23 0 x + 0 y = 46$

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

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

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In Problems 75– 82, algebraically solve each system of equations using any method you wish.
$\{\begin{cases} 2 x - 3 y + z = 4 \\ - 3 x + 2 y - z = 17 \\ - 5 y + z = 6 \end{cases}$

Short Answer

Step by step solution

Step 1. Given information

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

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In Problems 75– 82, algebraically solve each system of equations using any method you wish.2x-3y+z=4-3x+2y-z=17-5y+z=6

Short Answer

Step by step solution

Step 1. Given information

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Decision Maths

Theoretical and Mathematical Physics

Probability and Statistics

Geometry

Pure Maths

Study anywhere. Anytime. Across all devices.

In Problems 75– 82, algebraically solve each system of equations using any method you wish.
$\{\begin{cases} 2 x - 3 y + z = 4 \\ - 3 x + 2 y - z = 17 \\ - 5 y + z = 6 \end{cases}$