Use Cramer's rule to find the solution set of the system.

Question

Quizplus · Accepted Answer

Using Cramer's rule, we need to find the determinants of matrices formed by replacing the coefficients of x, y, and z with the constants on the right side.

D =

| 2  1  4 |
| 1  3  1 |
| 3 -2 -1 |

Dx =

| -6  1  4 |
|  3  3  1 |
|  2 -2 -1 |

Dy =

| 2 -6  4 |
| 1  3  1 |
| 3  2 -1 |

Dz =

| 2  1 -6 |
| 1  3  3 |
| 3 -2  2 |

Then, we can use the formulas:

x = Dx/D
y = Dy/D
z = Dz/D

where D is the determinant of the coefficient matrix.

Evaluating the determinants, we get:

D = -45
Dx = -33
Dy = -9
Dz = -45

Therefore, x = Dx/D = (-33)/(-45) = 5/3
y = Dy/D = (-9)/(-45) = 1/5
z = Dz/D = (-45)/(-45) = 1

So, the solution set is (5/3, 1/5, 1), which is equivalent to (15, 0.2, 1). The closest option is C, x = -5, y = 4, z = -4, which is not the answer.

Use Cramer's Rule to Find the Solution Set of the System