Question

Is the system of equations consistent and independent, consistent and dependent, or inconsistent? y=−3x 12y=−6x 2 Select the correct answer from the drop-down menu. Choose.

Answer 1

System of equations helps to compare two real-life situations. The system is an Independent Consistent System.

What is a System of the equation?

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,

$-3x + 12 = -6x + 2\\\\-3x + 6x = 2 -12\\\\3x = -10\\\\x = \dfrac{-10}{3}$

We know the value of x, substitute the value of x in the equation of y,

$y = -6x + 2\\\\y = -6(\dfrac{-10}{3}) + 2\\\\y = +20 + 2\\\\y = 22$

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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