Question

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Solve the system of equations using determinants.

3x + 2y = 7

3x - y = -8

Find the values of determinants D, Dx and Dy

D=?
Dx=?
Dy=?

Answer 1

To find the values of determinants, we first need to set up the coefficient matrix and the constant matrix:

Coefficient matrix:

| 3 2 |

| 3 -1 |

Constant matrix:

| 7 |

| -8 |

Now, we can use determinants to solve for the values.

D = | 3 2 | = (3 * -1) - (2 * 3) = -9

| 3 -1 |

Dx = | 7 2 | = (7 * -1) - (2 * -8) = -1

|-8 -1 |

Dy = | 3 7 | = (3 * -1) - (7 * 3) = -24

| 3 -8 |

Therefore, D = -9, Dx = -1, and Dy = -24