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System of equations helps to compare two real-life situations. The system is an 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 = −3x + 12
y = −6x + 2
As we have the value of y in both equations equate it against each other,
[tex]-3x + 12 = -6x + 2\\\\-3x + 6x = 2 -12\\\\3x = -10\\\\x = \dfrac{-10}{3}[/tex]
We know the value of x, substitute the value of x in the equation of y,
[tex]y = -6x + 2\\\\y = -6(\dfrac{-10}{3}) + 2\\\\y = +20 + 2\\\\y = 22[/tex]
As the value of both x and y is unique, therefore, there is a unique solution for the given system of equations.
Thus, the system has a unique solution, therefore, the system is an Independent Consistent System.
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