Question 332612
Solve the system of equations. Let z be the parameter. 
<pre><font size = 4 color = "indigo"><b>
{{{system(x+2y+3z=11,
2x-y+z=2)}}}

Get the constants and parameter variable terms on the right

{{{system(x+2y=11-3z,
2x-y=2-z)}}}

Eliminate y by multiplying the second equation through by 2:

{{{system(x+2y=11-3z,
4x-2y=4-2z)}}}


Add corresponding terms:

{{{5x=15-5z}}}

Divide through by 5:

{{{5x/5=15/5-5z/5}}}

{{{x=3-z}}}

Substitute in 

{{{x+2y=11-3z}}}


{{{(3-z)+2y=11-3z}}}

{{{3-z+2y=11-3z}}}

{{{2y=8-2z}}}

Divide through by 2:

{{{2y/2=8/2-2z/2}}}

{{{y=4-z}}}

So the solution is (x,y) = (3-z,4-z)

Edwin</pre>