Q.Solve the following equations using Crammer's rule : $4x + 3y = 8$ $6x + 7y = 17$

With $D=10$, $D_x=5$, $D_y=20$, Cramer's rule gives $x=\tfrac{1}{2}$, $y=2$.

The system is $4x+3y=8$ and $6x+7y=17$.

Step 1 — coefficient determinant $D$:

$D=\begin{vmatrix} 4 & 3 \\ 6 & 7 \end{vmatrix}=(4)(7)-(3)(6)=28-18=10$

Since $D=10\neq 0$, a unique solution exists.

Step 2 — $D_x$ (replace the $x$-column by the constants $8,17$):

$D_x=\begin{vmatrix} 8 & 3 \\ 17 & 7 \end{vmatrix}=(8)(7)-(3)(17)=56-51=5$

Step 3 — $D_y$ (replace the $y$-column by the constants):

$D_y=\begin{vmatrix} 4 & 8 \\ 6 & 17 \end{vmatrix}=(4)(17)-(8)(6)=68-48=20$

Step 4 — apply Cramer's rule:

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