Question 1044650
I will assume that your first equation is actually x+y+az = 0.

Simply equate the determinant of the coefficient matrix to 0:


===> {{{abs(matrix(3,3,1,1,a,1,1,b,a,b,1)) = 1+ab+ab-(a^2+b^2+1) = 0}}}

===> {{{-a^2 +2ab - b^2 = -(a^2-2ab+b^2) = -(a-b)^2 = 0}}}

===> {{{a = b}}}, for the system to have a non-trivial solution.