Why Math.?
The equation : 2 × y = 10
has only One Solution in the set of real numbers.Think of it as :what number when doubled
becomes 10.(You probably knew that 5 is the answer).
Yet this is not the only case for equations of this type (they are called:Equations of first degree in One unknown).
As you may know,any real number when multiplied by Zero gives you Zero as an answer,
suppose I asked you to find a real number when multiplied by Zero gives you 5 ,of course
you would say Impossible.
The situation would be like : 0 × y = 5
There is no real number y satisfying this condition,simply because:
0 × y = 0 for every real number y.
We say this equation has no (real) solution.
On the other hand,any real number when multiplied by Zero gives you Zero as an answer,
for e.g. 0 × 0 = 0 , 0 × 1 = 0 , 0 × 2 = 0 , etc......
You may have already figured out that this type of equation has Many solutions.
In fact the equation: 0 × y = 0 has an infinite number of solutions,
any real number could be y.
As a result : the equation a × y = b
has: One Solution, or Infinite number of solutions or No solution.
This does not only apply for Equations of the first degree in One unknown,it applies for yours,mine and everybody's daily life.It is the basic function of Human's lives to look for solutions and most frequently faced with situations where they have only one solution or many solutions or no solution at all.You may think of thousands of situations where you had to find a solution for certain problems you might have faced in your daily life operations.
Problem solving is a way of life, a methodology that applies for situations taking place in Humans lives not only formulas and numbers.