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Examine the consistency of the system of equation \(2x - y = 5;\,\,x + y = 4\)
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Examine the consistency of the system of equation \(2x - y = 5;\,\,x + y = 4\)

Answer

Matrix form of given equations is AX = B
\(\Rightarrow \left[ {\begin{array}{*{20}{c}} 2&{ - 1} \\ 1&1 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} x \\ y \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 5 \\ 4 \end{array}} \right]\)
\(\therefore A = \left[ {\begin{array}{*{20}{c}} 2&{ - 1} \\ 1&1 \end{array}} \right]\) and \(B = \left[ {\begin{array}{*{20}{c}} 5 \\ 4 \end{array}} \right]\)
\(\therefore \left| A \right| = \left| {\begin{array}{*{20}{c}} 2&{ - 1} \\ 1&1 \end{array}} \right| = 2 - \left( { - 1} \right) = 3 \ne 0\)
Therefore, Unique solution and hence, equations are consistent.
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