The last equation says <em>z</em> = 3, so that in the second equation we get
<em>y</em> + 2<em>z</em> = <em>y</em> + 6 = 5 ==> <em>y</em> = -1
and in turn, the first equation tells us
<em>x</em> - 2<em>y</em> + 2<em>z</em> = <em>x</em> + 2 + 6 = <em>x</em> + 8 = 9 ==> <em>x</em> = 1
So the solution to the system is (<em>x</em>, <em>y</em>, <em>z</em>) = (1, -1, 3).