Chapter: Linear Equations in Two Variables· Mathematics Part 1 (Algebra)
Answer: \(x = 2,\ y = -3\)
\(D = \begin{vmatrix} 5 & 2 \\ 3 & -4 \end{vmatrix} = -20 - 6 = -26\)
\(D_x = \begin{vmatrix} 4 & 2 \\ 18 & -4 \end{vmatrix} = -16 - 36 = -52\)
\(D_y = \begin{vmatrix} 5 & 4 \\ 3 & 18 \end{vmatrix} = 90 - 12 = 78\)
\(x = \dfrac{D_x}{D} = \dfrac{-52}{-26} = 2\), \(y = \dfrac{D_y}{D} = \dfrac{78}{-26} = -3\)
Check: \(5(2) + 2(-3) = 4\) ✓, \(3(2) - 4(-3) = 18\) ✓.