Question 670879
3 variables and 3 unknowns says you might have a solution. It doesn't mean there MUST be one.

take the first and third equations and add them
{{{x + y + z = 0}}}
{{{x -y + z = 2}}}
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{{{2x + 2y = 2}}} remember this

Now look at the second equation
{{{2x + 3y + 2x = -1}}}
{{{(2x+2z) + 3y = -1}}} sub in from above
{{{2 + 3y = -1}}}
{{{3y = -3}}}
{{{y = -1}}}

Plug y into the three original equtions, shows all three equations to be the same equation. So 1 equation with 2 unknowns, and you can;t solve that.

Another wya to look at this, solve the first and third equations for y
{{{x + z = -y}}}
{{{x + z = y}}}
the only way that works is y=0.
If you set y = 0 in the first anf thrid equations, the {{{x+z =0}}} and {{{x+z = 2}}} clearly that can't be,

So there is no solution to this one.