Question

solve the following simultaneous equations by using Cramer's rule:
$x+y=7,x-y=5$

Answer 1

The given equations are
$x+y=7$
$x-y=5$
$D=\left|\begin{array}{cc}1& 1\\ 1& -1\end{array}\right|=(1\times -1)-(1\times 1)=-1-1=-2$
$D_x=\left|\begin{array}{cc}7& 1\\ 5& -1\end{array}\right|=(7\times -1)-(1\times 5)=-7-5=-12$
$D_y=\left|\begin{array}{cc}1& 7\\ 1& 5\end{array}\right|=(1\times 5)-(7\times 1)=5-7=-2$
$\therefore$ By cramer's rule we get
$\therefore$ $x=\frac{D_x}{D}=\frac{-12}{2}=6$ and $y=\frac{D_y}{D}=\frac{-2}{2}=1$