Examine the consistency of the system of equa | vedclass

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

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Consistent

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(A) The given system of equations is:$x+2y=2$$2x+3y=3$The system can be written in the matrix form $AX=B$,where:$A = \begin{bmatrix} 1 & 2 \ 2 & 3 \end{bmatrix}$,$X = \begin{bmatrix} x \ y \end{bmatrix}$,$B = \begin{bmatrix} 2 \ 3 \end{bmatrix}$Now,calculate the determinant of $A$:$|A| = (1)(3) - (2)(2) = 3 - 4 = -1$Since $|A| 
eq 0$,the matrix $A$ is non-singular and invertible.Therefore,the system of equations has a unique solution and is consistent.

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

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