Answer
$\{ (1,-5,-6) \}$
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)
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(1.) Perform elimination by addition method (eliminate z) by
$Eq.$2 already is without x.
$-2Eq.1+Eq.3 \Rightarrow$
$(-2+2)x+(1-2)y+(3-0)z=-21+8$
$\left[\begin{array}{ll}
y-z=1 & I\\
-y+3z=-13 & II
\end{array}\right.$ ,
({\it 2}.) ... $I+II$ eliminates $y$:
$2z=-12$
$z=-6$
Back-substitute into $y-z=1$
$y-(-6)=1$
$y=1-6$
$y=-5$
(3.) Back-substitute into one of the initial equations:
$x+y=-4$
$x-5=-4$
$x=1$
Solution set: : $\{ (1,-5,-6) \}$
