Q.Using Cramer's Rule, the value of $x$ satisfying the system $2x+y=5$ and $x-y=1$ is:

Cramer's Rule gives $x$ as the ratio $D_x/D$, computed from the coefficient determinant and the determinant with the $x$-column replaced by the constants. …

The coefficient determinant is $D=\begin{vmatrix} 2 & 1 \\ 1 & -1 \end{vmatrix} = (2)(-1)-(1)(1) = -2-1=-3.$

Replacing the $x$-column with the constants $(5,1)$: $D_x=\begin{vmatrix} 5 & 1 \\ 1 & -1 \end{vmatrix} = (5)(-1)-(1)(1) = -5-1=-6.$

By Cramer's Rule, $x = \frac{D_x}{D} = \frac{-6}{-3} = 2.$ …

A common slip in MCQs of this type is computing $D$ or $D_x$ correctly but then forgetting to divide, mistakenly selecting the value of $D_x$ itself (he …