Answer:
x = -1, y = 2, z = 1
Explanation:
* note
we will solve the simultaneous equation using the Gaussian Elimination
[tex]x + 2y - z = 2\\3x - y + 2z =-3\\2x + 3y + z = 5[/tex]
[tex]\left[\begin{array}{cccc}1&2&-1&2\\3&-1&2&-3\\2&3&1&5\end{array}\right][/tex]
[tex]\left[\begin{array}{cccc}1&2&-1&2\\0&-7&5&-9\\2&3&1&5\end{array}\right][/tex]
[tex]\left[\begin{array}{cccc}1&2&-1&2\\0&-7&5&-9\\0&-1&3&1\end{array}\right][/tex]
[tex]\left[\begin{array}{cccc}1&2&-1&2\\0&-7&-\displaystyle\frac{5}{7} &-\displaystyle\frac{9}{7} \\0&-1&3&1\end{array}\right][/tex]
[tex]\left[\begin{array}{cccc}1&0&\displaystyle\frac{3}{7} &-\displaystyle\frac{4}{7} \\0&-7&-\displaystyle\frac{5}{7} &-\displaystyle\frac{9}{7} \\0&-1&3&1\end{array}\right][/tex]
[tex]\left[\begin{array}{cccc}1&0&\displaystyle\frac{3}{7} &-\displaystyle\frac{4}{7} \\0&-7&-\displaystyle\frac{5}{7} &-\displaystyle\frac{9}{7} \\0&0&\displaystyle\frac{16}{7} &\displaystyle\frac{16}{7} \end{array}\right][/tex]
[tex]\left[\begin{array}{cccc}1&0&0&-1 \\0&1&0} &2 \\0&0&1 &1\end{array}\right][/tex]
[tex]x = -1, y = 2, z =1[/tex]
