Chapter 2.5, Problem 55E

To determine

To find: solutions for the given system of equations.

Answer to Problem 55E

Infinite solutions

Explanation of Solution

Given information:

  $\begin{array}{c}x-3y+2z=6 \mathrm{...}\left(1\right)\\ 4x+y-z=8 \mathrm{...}\left(2\right)\\ -7x-5y+4z=-10 \mathrm{...}\left(3\right)\end{array}$

Calculation:

Multiply equation (2) by 2 and add t0 equation (1) to eliminate z as follows:

  $\begin{array}{l}x-3y+2z=6\\ 8x+2y-2z=16\\ \overline{9x-y=22}\end{array}$

Multiply equation (2) by 4 and add to equation (3) to eliminate z as follows:

  $\begin{array}{l}16x+4y-4z=32\\ -7x-5y+4z=-10\\ \overline{9x-y=22}\end{array}$

Since the resultant equations are same, so we will get $0=0$ on solving them. Thus, this system of equations has infinite solutions.