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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