Question 1101284
Add eq. 1 to eq. 3 to eliminate x,
{{{-2x+2y+3z+2x+3y+3z=0+5}}}
4){{{5y+6z=5}}}
Add eq. 2 to eq. 3 to eliminate x,
{{{-2x - y + z 2x+3y+3z=-3+5}}}
{{{2y+4z=2}}}
5){{{y+2z=1}}}
Multiply eq. 5 by 5 and subtract from eq. 4 to eliminate y.
{{{5y+6z-5y-10z=5-5}}}
{{{-4z=0}}}
{{{z=0}}}
So now work backwards to find z.
{{{y+2(0)=1}}}
Solve for y. 
Then use any one of the three original equations to solve for x.