Use Cramer's Rule to solve the following system of linear equations:

Question

Quizplus · Accepted Answer

Using Cramer's rule, we have:

x = (det(Ax) / det(A))
y = (det(Ay) / det(A))

where det(A) is the determinant of the coefficient matrix, and det(Ax) and det(Ay) are obtained by replacing the corresponding column of A with the constants.

In this case, we have:

A = [[3, -1], [4, 2]]
Ax = [[-6, -1], [10, 3]]
Ay = [[3, -6], [4, 10]]

det(A) = (3 * 2) - (-1 * 4) = 10
det(Ax) = (-6 * 2) - (-1 * 10) = -2
det(Ay) = (3 * 2) - (-6 * 4) = 27

Therefore, the solution is:

x = - (det(Ax) / det(A)) = 2/5
y = (det(Ay) / det(A)) = 27/10

So, the correct choice is (C).

Use Cramer's Rule to Solve the Following System of Linear