Question

Solve the simultaneous linear equations

$2x-5y=1,5x+3y=18$.

Answer 1

Given system of equations can be writtten in matrix form as shown :

$\left[\begin{array}{cc}2& -5\\ 5& 3\end{array}\right]\left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{c}1\\ 18\end{array}\right]$ or $AX=B$

Now,

$X=\left[\begin{array}{c}x\\ y\end{array}\right]={\left[\begin{array}{cc}2& -5\\ 5& 3\end{array}\right]}^{-1}\left[\begin{array}{c}1\\ 18\end{array}\right]$

$X=\frac{1}{31}\left[\begin{array}{cc}3& 5\\ -5& 2\end{array}\right]\left[\begin{array}{c}1\\ 18\end{array}\right]$

$X=\frac{1}{31}\left[\begin{array}{c}93\\ 31\end{array}\right]=\left[\begin{array}{c}3\\ 1\end{array}\right]$

Thus,

$X=\left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{c}3\\ 1\end{array}\right]$

Therefore,

$x=3$ and $y=1$