Solve the system of equations by Cramer's rule

Question

4x - 3y = 11 and 6x + 5y =7

Answer 1

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

Δ_x = \(\begin{vmatrix} {11} & {-3} \\ {7}& {5} \\ \end{vmatrix}\) = 55 + 21 = 76

Δ_y =\(\begin{vmatrix} {4} & {11} \\ {6}& {7} \\ \end{vmatrix}\) = 28 - 66 = -38

x = \(\frac{Δx}{Δ}\) = \(\frac{76}{38}\) = 2, y = \(\frac{Δy}{Δ}\) = \(\frac{-38}{38}\) = -1

solution is (2,-1)