Write the equations' coefficients as a matrix. Let the rows of the matrix represent each equation and the columns of the matrix represent the variables. For example, if you have the equations -2x + 3y = 8 and 3x - y = -5, you should create a matrix with two rows (because you have two equations) and two columns (because you have two variables: x and y). Row one will be [-2 3] and row two will be [3 -1].
Create a column vector that contains the numerical values of the equations. The numerical values are the numbers that are not accompanied by the variables. In our previous example, these numbers were 8 and -5 for the two equations. Thus, you create a column vector (a matrix with multiple rows but only one column) that contains 8 and -5. Call this column vector "c."
Find the inverse of the coefficient matrix. This is a complicated process that requires mathematical software. Use your mathematical software's inverse matrix function to compute the inverse of the coefficient matrix. Call this matrix "Inv."
Multiply the inverse of the coefficient matrix by the column vector. Use the matrix multiplication function in your math software. Make sure that the matrix comes before the column vector in this calculation. For example, many software programs use the symbol "*" for matrix multiplication, so in this software you would type "Inv*c". The result will be a column vector.
Interpret the column vector as a solution. The column vector's number of rows will be equal to the number of variables in your equations; the rows correspond to the variables. If you followed the example, your final column vector will contain the values -1 and 2. Thus, the solutions are x = -1 and y = 2.