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PLEASE HELP ME‼️(IMAGE ATTACHED)

Solve the system of equations using determinants.

3x + 5y = 27

2x - y = -8

Find the values of determinants D, Dx and Dy

D=?
Dx=?
Dy=?

PLEASE HELP ME‼️(IMAGE ATTACHED) Solve the system of equations using determinants-example-1

1 Answer

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Answer:

To solve the system of equations using determinants, we can use Cramer's Rule, which states that:

x = Dx / D

y = Dy / D

where Dx and Dy are the determinants obtained by replacing the x-coefficients and y-coefficients with the constants in the system, and D is the determinant of the coefficients.

In matrix form, the system can be written as:

| 3 5 | | x | | 27 |

| 2 -1 | x | y | = |-8 |

The determinant of the coefficients is:

D = | 3 5 |

| 2 -1 | = (3)(-1) - (5)(2) = -13

To find Dx, we replace the x-coefficients with the constants:

Dx = | 27 5 |

|-8 -1 | = (27)(-1) - (5)(-8) = -7

To find Dy, we replace the y-coefficients with the constants:

Dy = | 3 27 |

| 2 -8 | = (3)(-8) - (27)(2) = -66

Therefore, the values of the determinants are:

D = -13

Dx = -7

Dy = -66

Using Cramer's Rule, we can now find the values of x and y:

x = Dx / D = -7 / (-13) = 7/13

y = Dy / D = -66 / (-13) = 66/13

So the solution to the system of equations is:

x = 7/13

y = 66/13

Explanation:

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