Examine the consistency of the system of equa | vedclass

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(B) The given system of equations is:$x+3y=5$$2x+6y=8$The system can be written in the form $AX=B$,where:$A = \begin{bmatrix} 1 & 3 \ 2 & 6 \end{bmat

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Inconsistent

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(B) The given system of equations is:$x+3y=5$$2x+6y=8$The system can be written in the form $AX=B$,where:$A = \begin{bmatrix} 1 & 3 \ 2 & 6 \end{bmatrix}, X = \begin{bmatrix} x \ y \end{bmatrix}, B = \begin{bmatrix} 5 \ 8 \end{bmatrix}$First,we calculate the determinant of $A$:$|A| = (1)(6) - (3)(2) = 6 - 6 = 0$Since $|A| = 0$,the matrix $A$ is singular. We now calculate $(adj A)B$:$adj A = \begin{bmatrix} 6 & -3 \ -2 & 1 \end{bmatrix}$$(adj A)B = \begin{bmatrix} 6 & -3 \ -2 & 1 \end{bmatrix} \begin{bmatrix} 5 \ 8 \end{bmatrix} = \begin{bmatrix} 30 - 24 \ -10 + 8 \end{bmatrix} = \begin{bmatrix} 6 \ -2 \end{bmatrix} 
eq \begin{bmatrix} 0 \ 0 \end{bmatrix}$Since $(adj A)B 
eq 0$,the system of equations has no solution.Therefore,the system is inconsistent.

Examine the consistency of the system of equations: $x+3y=5$ and $2x+6y=8$.

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