Chapter 5, Systems of Equations and Inequalities - Section 5.2 - Systems of Linear Equations in Several Variables - 5.2 Exercises - Page 455: 33

$x=3-t$ $y=-3+2t$ $z=t$

Step 1. $x+y-z=0$ $x+2y-3z=-3$ Equation 2 $+$ $(-1)$ Equation 1 $2x+3y-4z=-3$ Equation 3 $+$ $(-2)$ Equation 1 Step 2. $x+y-z=0$ Equation 1 $+$ $(-1)$ Equation 2 $y-2z=-3$ $y-2z=-3$ Step 3. $x+z=3$ $y-2z=-3$ Step 4. Let $z=t$ $x=3-z=3-t$ $y=-3+2z=-3+2t$ Step 5. Conclude the solution. The solution is $x=3-t$, $y=-3+2t$, $z=t$.