Find the solution of the given system of linear equations by matrix method.

2x - 3y = 10

4x - 6y = 7

Ax = B

\(\left[ {\begin{array}{*{20}{c}} 2&{ - 3}\\ 4&{ - 6} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} x\\ y \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} {10}\\ 7 \end{array}} \right]\)

X = (adj(A).B)/(|A|)

|A| \(= \left| {\begin{array}{*{20}{c}} { - 6}&3\\ { - 4}&2 \end{array}} \right|\) = - 12 - (- 12) = - 12 + 12 = 0

|A| = 0

Adj (A) = \(\left[ {\begin{array}{*{20}{c}} { - 6}&3\\ { - 4}&2 \end{array}} \right]\)

\(X = \left[ {\begin{array}{*{20}{c}} { - 6}&3\\ { - 4}&2 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {10}\\ 7 \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} { - 60 + 21}\\ { - 40 + 14} \end{array}} \right]\)

0 = \(\left[ {\begin{array}{*{20}{c}} { - 39}\\ { - 26} \end{array}} \right]\)