Using determinant method to solve the simultane... - SS3 Mathematics Matrices and Determinants Question
Using determinant method to solve the simultaneous equations: \(2x + 3y = - 2\) and \(3x + 4y = - 6\)
\[\mathrm{\Delta} = \left| \begin{matrix} 2 & 3 \\ 3 & 4 \\ \end{matrix} \right| = 2(4) - 3(3) = 8 - 9 = - 1\]
\[\mathrm{\Delta}x = \left| \begin{matrix} 3 & - 2 \\ 4 & - 6 \\ \end{matrix} \right| = (3)( - 6) - ( - 2)4 = - 18 + 8 = - 10\]
\[\mathrm{\Delta}y = \left| \begin{matrix} 2 & - 2 \\ 3 & - 6 \\ \end{matrix} \right| = 2( - 6) - ( - 2)(3) = - 12 + 6 = - 6\]
\[x = \frac{\mathrm{\Delta}x}{\mathrm{\Delta}} = \frac{- 10}{- 1} = 10\]
\[y = \frac{\mathrm{\Delta}y}{\mathrm{\Delta}} = \frac{- 6}{- 1} = 6\]
Thus, \(x = 10\) and \(y = 6\)
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