Use Cramer's rule to find the solution for the system.

Question

Quizplus · Accepted Answer

Using Cramer's rule, we need to find the determinants of the coefficient matrix and the matrices formed by replacing the columns with the constants on the right-hand side.

The coefficient matrix is:
| 3  1 |
| 2 -2 |

The determinant of this matrix is: 
3(-2) - 1(2) = -8

Replacing the first column with the constants, we get:
| 4  1 |
| 2 -2 |

The determinant of this matrix is:
4(-2) - 1(2) = -10

Replacing the second column with the constants, we get:
| 3  4 |
| 2  1 |

The determinant of this matrix is:
3(1) - 4(2) = -5

Using Cramer's rule, we find that:
x = -10/-8 = 5/4
y = -5/-8 = 5/8

Therefore, the best choice is C: x = 2, y = 2.

Use Cramer's Rule to Find the Solution for the System