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4x - 3y = 11 and 6x + 5y =7 |
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Answer» 4x - 3y = 11;6x + 5y = 7 The matrix equation is \(\binom{4\,\,-3}{6\,\,-5}\) \(\binom{x}{y}\) = \(\binom{11}{7}\) A X = B Now Δ =\( \begin{vmatrix} {4} & {-3} \\ {6}& {5} \\ \end{vmatrix}\) = 20 + 18 = 38 ≠ 0 ∴ we can apply Cramer's rule Δx = \(\begin{vmatrix} {11} & {-3} \\ {7}& {5} \\ \end{vmatrix}\) = 55 + 21 = 76 Δy =\(\begin{vmatrix} {4} & {11} \\ {6}& {7} \\ \end{vmatrix}\) = 28 - 66 = -38 x = \(\frac{Δx}{Δ}\) = \(\frac{76}{38}\) = 2, y = \(\frac{Δy}{Δ}\) = \(\frac{-38}{38}\) = -1 solution is (2,-1) |
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