Solve the system of equations using determinants.
-x + 3y = 19 3y + 4x = 23
A) (-5, 2)
B) (5, 2)
C) (2, 5)
D) infinite number of solutions

Question

Quizplus · Accepted Answer

To solve using determinants, we need to set up the coefficient matrix and the constant matrix:

Coefficient matrix:
| 1  3 |
| 4  3 |

Constant matrix:
| 19 |
| 23 |

Now, we can use Cramer's rule to solve for x and y:

x = det(| 19  3 |) / det(| 1  3 |) = (19*3 - 3*23) / (1*3 - 3*4) = 2
y = det(| 1  19 |) / det(| 1  3 |) = (1*23 - 19*3) / (1*3 - 3*4) = 5

Therefore, the solution is (2, 5), which corresponds to choice C.

Solve the System of Equations Using Determinants