Question

Use the matrix method to solve the system of equations 2x + 4y = 8 and 6x + 3y = -3. The resulting matrix is:

Answer 1

So we are given the system:
$2x+4y=8\\ 6x+3y=-3$
Written in matrix form we get:
$\left[\begin{array}{cc}2&4\\6&3\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{c}8\\-3\end{array}\right]$
We compute the solution like this:
$\left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{cc}2&4\\6&3\end{array}\right] ^{-1} \left[\begin{array}{c}8\\-3\end{array}\right] \\= \left[\begin{array}{cc}-3&4\\6&-2\end{array}\right] \left[\begin{array}{c}8\\-3\end{array}\right] \dfrac{1}{18}\\= \left[\begin{array}{c}2\\-3\end{array}\right]$
The solution is :
$\left[\begin{array}{c}2\\-3\end{array}\right]$