Question

Solve the following equations by using Cramer's rule:
$3x+4y+5z=18$
$2x-y-8z=13$
$5x-2y+7z=20$

Answer 1

$3x+4y+5z=18$

$42x-y-8z=13$
$5x-2y+7z=20$

$\Delta =\left[\begin{array}{ccc}3& 4& 5\\ 2& -1& -8\\ 5& -2& 7\end{array}\right]$

$\Delta x=\left[\begin{array}{ccc}18& 4& 5\\ 13& -1& -8\\ 20& -2& 7\end{array}\right]$

$\Delta y=\left[\begin{array}{ccc}3& 8& 5\\ 2& 13& -8\\ 5& 20& 7\end{array}\right]$

$\Delta z=\left[\begin{array}{ccc}3& 4& 18\\ 2& -1& 13\\ 5& -2& 20\end{array}\right]$

On solving $\Delta =-280,\Delta x=-1448,\Delta y=-344,\Delta z=136$

So $x=\frac{\Delta x}{\Delta }=\frac{-1448}{-280}=\frac{181}{35}$

$y=\frac{\Delta y}{\Delta }=\frac{-344}{-280}=\frac{43}{35}$

$z=\frac{\Delta z}{\Delta }=\frac{136}{-280}=\frac{-17}{35}$