![]() On the other hand, the system of linear equations will have infinitely many solutions if the given equations represent line or plane in 2 and 3 dimensions respectively. For a 3 dimensional case, the given system of equations represents parallel planes. A case of no solution means that the two lines never intersect such lines are parallel to each other.Ĭlearly, the two lines are parallel and therefore they will never intersect. ![]() Viewing the equations as straight lines in a 2d graph, a solution to the system is a point where the two lines intersect. On the other hand the system will have infinitely many solutions if its determinant equal to zero.įor a system of equations with 2 unknowns, you need two equations to solve the system. Given any non-homogenous system of linear equation (n*n), the system will have a unique solution (non-trivial) if and only if the determinant of its coefficient matrix is non-zero. Solving systems of equations calculator Online When a system of linear equations does have a unique solution?
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