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)