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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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