Question 1091457
<br>The first equation says x+y+z is equal to 4; the second says x+y-z is also equal to 4.  Either by logical reasoning or by formal algebra, that means z must be 0.<br>
So now the first two equations both say x+y is 4; and the third says 3x+3y is 12.  But that third equation is then equivalent to the other two.<br>
We know z is 0; and all we know about x and y is that their sum is 4.  So we can't find a single solution; there is an infinite family of solutions.
{{{x+y = 4}}}  -->  {{{y = 4-x}}}
So we can choose any value for x, and then the corresponding y value is 4 minus the x value we chose.  Algebraically, there are an infinite set of solutions defined using parameter x as follows:
{{{x = x}}}
{{{y = 4-x}}}
{{{z = 0}}}