I was wondering if someone could double check my work on a test I'm self correcting. Here's the problem, it has to do with Cramer's Rule.
24x + 6y = 11
24x + 60y = -25
I ended up finding the base determinant (D), and then dividing Dx and Dy by D. My answers for Dx and Dy checked out correctly. Here's what I got ultimately.
(.625, -.666)
as in, x = .625, y = -.666
I think that's correct, but the decimals are throwing me off and I'm not %100 percent sure.
that's what I get.
What's wrong with 5/8 and -2/3 ?
It's not always necessary to reduce to decimal values. √2 is exact; 1.414 is not.
To double-check your work using Cramer's Rule, we need to find the determinants D, Dx, and Dy.
Given the system of equations:
24x + 6y = 11
24x + 60y = -25
First, let's find the base determinant D:
D = determinant of the coefficient matrix
= |24 6|
|24 60|
Using the formula for the determinant of a 2x2 matrix:
D = (24 * 60) - (6 * 24)
= 1440 - 144
= 1296
Next, let's find the determinant Dx:
Dx = determinant of the matrix formed by replacing the coefficients of x with the constants
= |11 6|
|-25 60|
Using the same formula as before:
Dx = (11 * 60) - (6 * -25)
= 660 + 150
= 810
Similarly, let's find the determinant Dy:
Dy = determinant of the matrix formed by replacing the coefficients of y with the constants
= |24 11 |
|24 -25|
Dy = (24 * -25) - (11 * 24)
= -600 - 264
= -864
Now, let's calculate the values of x and y:
x = Dx / D
= 810 / 1296
≈ 0.625
y = Dy / D
= -864 / 1296
≈ -0.666
Therefore, your values for x and y are approximately x = 0.625 and y = -0.666. Your solution appears to be correct!