Is there simultaneous equation which cant be solved?

Answer 1

By definition, there cannot be a simultaneous equation that cannot be solved, there must be a set of simultaneous equations. It is important to realise that simultaneous equations need not be linear.

It is simple to devise a pair of linear equations that are inconsistent:

x + y = 1 and x + y = 2

There is no solution. Graphically, the two lines are parallel.

Another possibility is

x + y = 1 and 2x + 2y = 2

In this case there are an infinite number of solutions. Graphically, the two lines are coincidet, so that every point on the common line is a solution. There is, therefore, no unique solution.

Yet another situation can arise when the domain of the equations is restricted.

For example,

x2 + y2 = -1 where x and y are real along with any other equation in x and y.