To represent a 2x2 system of equations with matrix notation, the first step is to write a 2x2 matrix with the coefficients of the system.
Each row of the coefficient matrix corresponds to the coefficients of one of the equations:
[tex]\begin{bmatrix}{1} & {2} \\ {2} & {3}\end{bmatrix}[/tex]
Then, the variable matrix is a 2x1 matrix (it is a column). The entries of that matrix are x and y:
[tex]\begin{bmatrix}{x} \\ {y}\end{bmatrix}[/tex]
Finally, the constant matrix is a 2x1 matrix with the constants at the right hand side of each of the equations.
[tex]\begin{bmatrix}{11} \\ {18}\end{bmatrix}[/tex]
To write the system as a matrix equation, set the coefficient matrix multiplied by the variable matrix equal to the constant matrix:
[tex]\begin{bmatrix}{1} & {2} \\ {2} & {3}\end{bmatrix}\begin{bmatrix}{x} \\ {y}\end{bmatrix}=\begin{bmatrix}{11} \\ {18}\end{bmatrix}[/tex]
