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There is only one type of solution if there are two linear equations. and that is the point of intersection listed in (x,y) form.
No, analytical solutions do not always exist. That is to say, the answer need not be a function. However, it is possible to find numerical solutions.
She did not figure out a particular equation but found the set of conditions under which solutions to a class of partial differential equations would exist. This is now known as the Cauchy-Kovalevskaya Theorem.
zero solutions. If you plot these two lines, you will see that they are parallel and do not intersect.
Let the number of unknowns be N. The solution space may have N, N-1, ..., 0 dimensions or may not exist. If a solution exists and the dimension of the solution space is 0, then there is exactly one solution,. If the dimension of the solution space > 0, then there are infinitely many solutions.