x+y=0
2x+2y=0
This homogeneous system has infinitely many non-trivial solutions.
If you are looking for exactly one non-trivial solution, no such system exists. the system may or may not have non trivial solution. if number of variables equal to number of equations and given matrix is non singular then non trivial solution does not exist
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Any solution to a system of linear equations must satisfy all te equations in that system. Otherwise it is a solution to AN equation but not to the system of equations.
They make up the solution set.
No, this is not necessarily the case. A function can have an infinite range of solutions but not an infinite domain. This means that not every ordered pair would be a solution.
Without any equality signs the given expressions can't be considered as equations.
Yes you can, if the solution or solutions is/are real. -- Draw the graphs of both equations on the same coordinate space on the same piece of graph paper. -- Any point that's on both graphs, i.e. where they cross, is a solution of the system of equations. -- If both equations are linear, then there can't be more than one such point.