Use the matrix method to solve the system of equations 2x + 4y = 8 and 6x + 3y = -3. The resulting matrix is:1 0 -20 1 31 0 20 1 30 1 -21 0 3

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