Question

Use cramer's rule to determine if the system is inconsistent system or contains dependent equations. 2x + 7 = 8 6x + 3y = 24 question 24 options: system is inconsistent system contains dependent equations

Answer 1

Answer: In the equations that you have given, we have a dependent system.

2x + y = 8 (I assumed that you meant to type y instead of 7)
6x + 3y = 24


To use Cramer's Rule, we have to take the determinant of 3 different matrices written in the problem. Taking the determinant of the coefficient matrix produces a zero.

2 1 This is the coefficient matrix.
6 3

6 - 6 = 0

Since this is 0, the rest of the work will be undefined meaning the systems are dependent (or they are the versions of the same equation).

Answer 2

The given system of equation is neither inconsistent nor contains the dependent equation.

Explanation:

Given system of equation,

2x + 7y = 8,

6x + 3y = 24,

Since, the determinant of coefficients of variables,

`D=\begin{vmatrix}2 & 7 \\ 6 & 3\end{vmatrix}`

`=2* 3-7* 6`

`=6-42`

`=-36`

Since, D ≠ 0,

Hence, the given system of equation is neither inconsistent nor contains the dependent equation.