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## Solve the following simultaneous equations using Cramer’s rule. (4) 6x – 4y = –12 ; 8x – 3y = –2

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Sol.     Given equation are
6x  – 4y  =  –12
8x  – 3y  =  –2

D   =  $\begin{vmatrix} 6 & -4 \\ 8 & -3 \\ \end{vmatrix}$

=  (6 × –3) – (–4 × 8)
=   –18 – (–32)
=   –18 + 32
=   14

∴       $D_x$  =  $\begin{vmatrix} -12 & -4 \\ -2 & -3 \\ \end{vmatrix}$

=  (–12 × –3) – (–4 × –2)
=   36 – 8
=   28

∴       $D_y$  =    $\begin{vmatrix} 6 & -12 \\ 8 & -2 \\ \end{vmatrix}$

=    (6 × –2) – (–12 × 8)
=    –12 – (–96)
=    –12 + 96

=     84

By Cramer’s Rule, we get;

∴         x   =   $D_x\over D$          and           y   =  $D_y\over D$

∴        x   =   $28\over 14$                    ∴   y   =   $84\over 14$

∴        x   =    2                     ∴    y  =   6

∴       (x, y) = (2, 6) is the solution of the  given equations.

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