First let . This is the matrix formed by the coefficients of the given system of equations.
Take note that the right hand values of the system are and which are highlighted here:
These values are important as they will be used to replace the columns of the matrix A.
Now let's calculate the the determinant of the matrix A to get . Remember that the determinant of the 2x2 matrix is . If you need help with calculating the determinant of any two by two matrices, then check out this solver.
Notation note: denotes the determinant of the matrix A.
Now replace the first column of A (that corresponds to the variable 'x') with the values that form the right hand side of the system of equations. We will denote this new matrix (since we're replacing the 'x' column so to speak).
Now compute the determinant of to get . Once again, remember that the determinant of the 2x2 matrix is
To find the first solution, simply divide the determinant of by the determinant of to get:
We'll follow the same basic idea to find the other solution. Let's reset by letting again (this is the coefficient matrix).
Now replace the second column of A (that corresponds to the variable 'y') with the values that form the right hand side of the system of equations. We will denote this new matrix (since we're replacing the 'y' column in a way).
