Answer:
x = 6.111... and y = 1.
Explanation:
To use Cramer's Rule, we first write the system of equations in matrix form, where the coefficients of x and y are placed in a matrix, and the constant terms are placed in a separate matrix. We then calculate the determinant of the coefficient matrix, which is the number that is obtained by multiplying the diagonal elements and subtracting the product of the off-diagonal elements.
Next, we replace the first column of the coefficient matrix with the constant terms and calculate the determinant of the resulting matrix. We do the same thing for the second column of the coefficient matrix. We then use Cramer's Rule to solve for x and y, which involves dividing the determinant of the matrix obtained by replacing the column of x coefficients with the constant terms by the determinant of the coefficient matrix to get the value of x. We do the same thing to find the value of y by dividing the determinant of the matrix obtained by replacing the column of y coefficients with the constant terms by the determinant of the coefficient matrix.
In the case of the given system of equations, the determinant of the coefficient matrix is 18. We then calculate the determinants of the matrices formed by replacing the first column of the coefficient matrix with the constant terms and the second column of the coefficient matrix with the constant terms. Using these determinants, we apply Cramer's Rule to find the values of x and y, which are x = 6.111... and y = 1.