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Solve this linear system using determinants: 2x 3y = 6 −8x − 3y = 12.

User Rplevy
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Answer: To solve the linear system using determinants, we can write the system of equations in matrix form:

| 2 3 | | x | | 6 |

| -8 -3 | | y | = | 12 |

The determinant of the coefficient matrix is calculated as follows:

D = | 2 3 |

| -8 -3 |

The determinant of a 2x2 matrix is calculated by taking the product of the main diagonal elements and subtracting the product of the off-diagonal elements:

D = (2 * -3) - (3 * -8)

D = -6 + 24

D = 18

Now, we will find the determinant of the x matrix, which is obtained by replacing the x column in the coefficient matrix with the constants:

Dx = | 6 3 |

| 12 -3 |

Dx = (6 * -3) - (3 * 12)

Dx = -18 - 36

Dx = -54

Next, we find the determinant of the y matrix, which is obtained by replacing the y column in the coefficient matrix with the constants:

Dy = | 2 6 |

| -8 12 |

Dy = (2 * 12) - (6 * -8)

Dy = 24 + 48

Dy = 72

Finally, we can solve for x and y using the determinants:

x = Dx / D

x = -54 / 18

x = -3

y = Dy / D

y = 72 / 18

y = 4

Therefore, the solution to the given linear system is x = -3 and y = 4.

User Pini Cheyni
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