## College Algebra (10th Edition)

$\left\{\begin{array}{lllll} x_{1} & & & +x_{4} & =-2\\ & x_{2} & & +2x_{4} & =2\\ & & x_{3} & -x_{4} & =0\\ & & & 0 & =0 \end{array}\right.$ The system is consistent. Solution set = $\{(x_{1},x_{2},x_{3},x_{4})\ |\ x_{1}=-2-x_{4},\ \ x_{2}=2-2x_{4}\ \ x_{3}=x_{4}, \ \ x_{4} \in \mathbb{R} \}$
The system represented by the augmented matrix is $\left\{\begin{array}{lllll} x_{1} & & & +x_{4} & =-2\\ & x_{2} & & +2x_{4} & =2\\ & & x_{3} & -x_{4} & =0\\ & & & 0 & =0 \end{array}\right.$ The last equation is always true. The system is consistent. Take $x_{4}\in \mathbb{R}$, (any real number) Equation 3 $\Rightarrow x_{3}=x_{4}$ Equation 2 $\Rightarrow x_{2}=2-2x_{4}$ Equation 1 $\Rightarrow x_{1}=-2-x_{4}$ Solution set = $\{(x_{1},x_{2},x_{3},x_{4})\ |\ x_{1}=-2-x_{4},\ \ x_{2}=2-2x_{4}\ \ x_{3}=x_{4}, \ \ x_{4} \in \mathbb{R} \}$