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
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.
A solution of any sort is a homogeneous mixture.
A homogeneous mixture, homo- means of the same. A homogeneous mixture is a mixture that cannot be separated in any way.
Any phase is distinct.
row reduce the matrix in question and see if it has any free variables. if it does then it has many solution's. If not then it only has one unique solution. which is of course the trivial solution (0)
Homogeneous means that a material is the same throughout. Samples taken from any part of the material will be identical to one another. Elements and compounds are homogeneous pure substances. Solutions are homogeneous mixtures.
Any true solution provides an example of a homogeneous mixture, as do most metal alloys such as brass and bronze.
The purpose is to obtain a homogeneous mixture.
I think you mean a homogeneous mixture. Its because sugar is completely dissolved in water, so it will not be visible anymore, therefore, they become with only one phase or as you call it... a 'clear solution'
Each crystallic particle is pure NaCl, homogeneous.
Any part of a system with uniform composition and properties is called a phase ant it is always true.
A Saturated Solution. In an unsaturated solution, more will dissolve, but once the solution is saturated, it is "full" and will not allow any material to dissolve in it at current temperature and other conditions.
No nontrivial program is bug free. Freeware or Commercial.