Answer
$\{ (2,2,2) \}$
Work Step by Step
Plan (see p.533):
1. Eliminate one variable and arrive at a system of two equations in two variables.
2. Solve the system of two equations in two variables.
3. Back-substitute the solutions of (2) to find the eliminated varable in (1)
------------
(1.) Perform elimination by addition method (eliminate $y$) by
$Eq.2$ already is without x.
$Eq.1-Eq.3 \Rightarrow$
$(1-0)x+(1-1)y+(0-1)z=4-0$
$\left[\begin{array}{ll}
x+z=4 & I\\
x-z=0 & II
\end{array}\right.$ ,
({\it 2}.) ... $I+II$ eliminates $z$:
$2x=4$
$z=2$
Back-substitute into $x+z=4$
$x+z=4$
$x=2$
(3.) Back-substitute into one of the initial equations:
$y+z=4$
$y+2=4$
$y=2$
Solution set: : $\{ (2,2,2) \}$
