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For the determinant of dependent coefficients is equal to 0, it means that one equation of the system is a multiple of the other and therefore the system of linear equations is inconsistent and solutions do not exists.
In this question we find a system of two linear equations with two variables, which means the possibility of one solution only.
There are several methods to resolve this system and we have chose the determinant method which offers a visual-like and efficient method. Now we proceed to present the procedure:
Determinant of the matrix of dependent coefficients
[tex]D = \left[\begin{array}{cc}3&6\\1&2\end{array}\right][/tex]
D = 3 · 2 - 1 · 6
D = 0
For the determinant of dependent coefficients is equal to 0, it means that one equation of the system is a multiple of the other and therefore the system of linear equations is inconsistent and solutions do not exists.
To learn more on determinants: https://brainly.com/question/22247684
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