Step 1

Let x1=x , x2=y and x3=z

So, the equations are:

2x-y-z=-3

3x+2y+z=13

x+2y+2z=11

Step 2

Let use eliminate z first. Add first two equations. That gives 5x+y=10

Step 3

Multiply first equation by 2 and add it to the third equation.

\(\displaystyle{2}{\left({2}{x}-{y}-{z}=-{3}\right)}\Rightarrow{4}{x}-{2}{y}-{2}{z}=-{6}\)

Add it to x+2y+2z=11

So we get 5x=5

So, \(\displaystyle{x}=\frac{{5}}{{5}}={1}\)

Step 4

We had 5x+y=10

Here we plug x=1 and find y

5(1)+y=10

Or, 5+y=10

Or, y=5

Step 5

In 2x-y-z=-3 we plug x=1 and y=5 and find z

2(1)-5-z=-3

Or, 2-5-z=-3

Or, -3-z=-3

Or, z=0

Result: \(\displaystyle{\left({x}_{{1}},{x}_{{2}},{x}_{{3}}\right)}={\left({1},{5},{0}\right)}\)

Let x1=x , x2=y and x3=z

So, the equations are:

2x-y-z=-3

3x+2y+z=13

x+2y+2z=11

Step 2

Let use eliminate z first. Add first two equations. That gives 5x+y=10

Step 3

Multiply first equation by 2 and add it to the third equation.

\(\displaystyle{2}{\left({2}{x}-{y}-{z}=-{3}\right)}\Rightarrow{4}{x}-{2}{y}-{2}{z}=-{6}\)

Add it to x+2y+2z=11

So we get 5x=5

So, \(\displaystyle{x}=\frac{{5}}{{5}}={1}\)

Step 4

We had 5x+y=10

Here we plug x=1 and find y

5(1)+y=10

Or, 5+y=10

Or, y=5

Step 5

In 2x-y-z=-3 we plug x=1 and y=5 and find z

2(1)-5-z=-3

Or, 2-5-z=-3

Or, -3-z=-3

Or, z=0

Result: \(\displaystyle{\left({x}_{{1}},{x}_{{2}},{x}_{{3}}\right)}={\left({1},{5},{0}\right)}\)