Question

Solve the following simultaneous equations using Cramer's rule .
(ii) $y=\frac{5x-10}{2}$ ; 4 x + 5 = $-$ y

Answer 1

The given equations are:

$y=\frac{5x-10}{2}$
⇒ 5x $-$2 y = 10 ----------(i)
and
4 x + 5 = $-$ y
⇒ 4 x + y = $-$ 5 ----------(ii)

Here, D = $\left|\begin{array}{cc}5& -2\\ 4& 1\end{array}\right|=5\times 1-\left(-2\right)\times 4=5+8=13$
Now, we have:
D_x =$\left|\begin{array}{cc}10& -2\\ -5& 1\end{array}\right|=10\times 1-\left(-2\right)\times \left(-5\right)=10-10=0$

D_y =$\left|\begin{array}{cc}5& 10\\ 4& -5\end{array}\right|=5\times \left(-5\right)-10\times 4=-25-40=-65$

By Cramer's rule, we get:

$$\begin{gathered} x=\frac{D_x}{D}=\frac{0}{13}=0 \\ \mathrm{and} \\ y=\frac{Dy}{D}=\frac{-65}{13}=-5 \\ \therefore x=0\mathrm{and}y=-5\mathrm{is}\mathrm{the}\mathrm{solution}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{simultaneous}\mathrm{equations}. \end{gathered}$$