System of Equations

We are going to understand what a linear equation is and what a system of linear equations is.

Let's see a glimpse of linear and non-linear equations.

Linear Equation:
a + b = 10
5a + 2b = 20
9.5a + 36.6b - 3c = 155.9

In a linear equation, a, b, c were allowed only to have numbers or the scalars attached to them.

Non-Linear Equation:
It can be square (i.e: a^2 + b^2 = 10)
Can have sin, cos, tan, arc tan { i.e: sin( a + c^10 = 18)}
Can have power ( i.e: 5^a - 2^b = 0)
and so on!

Now, Suppose:

_System-1: _
a +b = 10
a +2b = 12
Solving this two equation, it gives unique solution. So, it's a complete system and non-singular.

System-2
a + b = 10
2a + 2b = 20

Solving these two equations gives infinity many solutions because the two equations are exactly the same.
As in, we can consider it as:
a = 8, 7, 6
b = 2, 3, 4
So, it's redundant and singular.

System-3
a + b = 10
2a + 2b = 24

No solution here because two equations contradict each other.