Use Cramer's rule to find the solution for the system.
A) x = 7, y = 0
B) x = 4, y = 0
C) x = 2, y = 2
D) x = 3, y =2
E) x = 1, y = 5

Question

Use Cramer's rule to find the solution for the system. 
A) x = 7, y = 0 
B) x = 4, y = 0 
C) x = 2, y = 2 
D) x = 3, y =2 
E) x = 1, y = 5

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