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

Question

Quizplus · Accepted Answer

Using Cramer's Rule, we first find the determinant of the coefficient matrix, which is:

| 3  1 |  
| 1 -2 |

det = (3)(-2) - (1)(1) = -7

Next, we find the determinant of the matrix formed by replacing the first column with the constants on the right-hand side:

| 8  1 |  
|-5 -2 |

det(x) = (8)(-2) - (1)(-5) = -11

Similarly, we find the determinant of the matrix formed by replacing the second column with the constants:

| 3  8 |  
| 1 -5 |

det(y) = (3)(-5) - (8)(1) = -23

Finally, we use Cramer's Rule to obtain the values of x and y:

x = det(x)/det = -11/(-7) = 11/7
y = det(y)/det = -23/(-7) = 23/7

Therefore, the solution to the system of linear equations is (x,y) = (11/7, 23/7). Answer choice B matches this solution.

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