A system of linear equations can be expressed in matrix form using the structure \( AX = B \), where \( A \) is the coefficient matrix, \( X \) is the variable matrix, and \( B \) is the constants matrix. This format is efficient for solving systems of equations using matrix operations.
\[ \begin{pmatrix} a_1 x + b_1 y \\ a_2 x + b_2 y \end{pmatrix} = \begin{pmatrix} c_1 \\ c_2 \end{pmatrix} \]
This is a system of two linear equations written vertically, showing the expressions for each equation.
\[ \begin{pmatrix} a_1 & b_1 \\ a_2 & b_2 \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} c_1 \\ c_2 \end{pmatrix} \]
This is the compact matrix form: \( AX = B \), where the coefficient matrix multiplies the variable matrix to equal the constants matrix.