System of equations helps us to compare two different situations. The system is Independent Consistent System.
Inconsistent System
A system of equations to have no real solution, the lines of the equations must be parallel to each other.
Consistent System
1. Dependent Consistent System
A system of the equation to be Dependent Consistent System the system must have multiple solutions for which the lines of the equation must be coinciding.
2. Independent Consistent System
A system of the equation to be Independent Consistent System the system must have one unique solution for which the lines of the equation must intersect at a particular.
Given to us
y = 4x - 4
y = -4x + 4
As we have the two equations, substitute the value of y of both the equations,
4x - 4 = -4x + 4
8x = 8
x = 1
We have the value of x as 1, substitute the value of x in the equation of y,
y = 4(1) - 4
y = 0
Since the two equations have a unique solution, therefore, the system is Independent Consistent System.
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