Question

Solve the following simultaneous equations using Cramer's rule.
(iv) 3x + 2 y + 11 = 0 ; 7 x $-$ 4y = 9

Answer 1

The given equations are:

3x + 2 y + 11 = 0
⇒ 3x + 2 y = $-$ 11 ----------(i)
and
7 x $-$ 4y = 9 ----------(ii)

Here, D = $\left|\begin{array}{cc}3& 2\\ 7& -4\end{array}\right|=3\times \left(-4\right)-2\times 7=-12-14=-26$
Now, we have:

D_x =$\left|\begin{array}{cc}-11& 2\\ 9& -4\end{array}\right|=\left(-11\right)\times \left(-4\right)-2\times 9=44-18=26$

D_y =$\left|\begin{array}{cc}3& -11\\ 7& 9\end{array}\right|=3\times 9-\left(-11\right)\times 7=27+77=104$

By Cramer's rule, we get:

$$\begin{gathered} x=\frac{D_x}{D}=\frac{26}{-26}=-1 \\ \mathrm{and} \\ y=\frac{Dy}{D}=\frac{104}{-26}=-4 \\ \therefore x=-1\mathrm{and}y=-4\mathrm{is}\mathrm{the}\mathrm{solution}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{simultaneous}\mathrm{equations}. \end{gathered}$$