Question 153681
There are many ways to solve. 
We'll use elimination.
Combine the equations to get rid of one of the variables.  
1.{{{x+y-z=-1}}}
2.{{{-4x+(-y)+2z=-7}}}
3.{{{2x+(-2y)+(-5z)=7}}}
Add eq.1 and eq.2, to get rid of y.

{{{(x+y-z)+(-4x-y+2z)=-1-7}}}
4.{{{-3x+z=-8}}}
Multiply eq. 2 by (-2) and add it to 3
{{{-2(-4x-y+2z)+(2x-2y-5z)=-2(-7)+7}}}
{{{8x+2y-4z+2x-2y-5z=14+7}}}
5.{{{10x-9z=21}}}
Now you have two equations 4 and 5 in x and z.
Keep going.
Multiply eq. 4 by (9) and add to eq. 5 to get rid of z.
{{{9(-3x+z)+(10x-9z)=9(-8)+21}}}
{{{-27x+9z+10x-9z=-72+21}}}
{{{-17x=-51}}}
{{{highlight(x=3)}}}
Now that you have x you can work back to get z and then y.
5.{{{10x-9z=21}}}
{{{10(3)-9z=21}}}
{{{-9z=21-30}}}
{{{-9z=-9}}}
{{{highlight(z=1)}}}
Finally,
1.{{{x+y-z=-1}}}
{{{3+y-1=-1}}}
{{{2+y=-1}}}
{{{highlight(y=-3)}}}
This method will work with as many number of equations as you have although it does get more tedious and prone to making mistakes when the number of equations gets too large.