Chapter 1 - Systems of Linear Equations - 1.1 Introduction to Systems of Linear Equations - 1.1 Exercises - Page 10: 47

$x$=1, $y$=2, $z$=3

$x$ + $y$ + $z$ = 6 2$x$ - $y$ + $z$ = 3 3$x$ - $z$ = 0 -2$R_{1}$+$R_{2}$→$R_{2}$ $x$ + $y$ + $z$ = 6 -3$y$ - $z$ = -9 3$x$ - $z$ = 0 -3$R_{1}$+$R_{3}$→$R_{3}$ $x$ + $y$ + $z$ = 6 -3$y$ - $z$ = -9 -3$y$ - 4$z$ = -18 -$R_{2}$→$R_{2}$ $x$ + $y$ + $z$ = 6 3$y$ + $z$ = 9 -3$y$ - 4$z$ = -18 $R_{2}$+$R_{3}$→$R_{3}$ $x$ + $y$ + $z$ = 6 3$y$ + $z$ = 9 -3$z$ = -9 $z$ = 3, plug in $z$ into (3$y$ + $z$ = 9) 3$y$ + (3) = 9 $y$ = 2 $x$ + (2) + (3) = 6 $x$ = 1