Use Cramer's rule to solve this:

Question

3x+2y= 7 ----- (1)
5x-3y= 37 ----- (2)

Answer 1

To use Cramer's rule, we need to first find the determinant of the coefficient matrix and the determinant of the matrix formed by replacing the first column of the coefficient matrix with the constants from the right-hand side of the equations.

Coefficient matrix:
|3 2|
|5 -3|

Constants matrix (replacing first column):
|7 2|
|37 -3|

Determinant of coefficient matrix:
|3 2|
|5 -3| = (3)(-3) - (2)(5) = -9 - 10 = -19

Determinant of constants matrix (replacing first column):
|7 2|
|37 -3| = (7)(-3) - (37)(2) = -21 - 74 = -95

Now we can use Cramer's rule to solve for x and y:

x = (d_x/d)
where d_x is the determinant of the matrix formed by replacing the first column of the coefficient matrix with the constants from the right-hand side of the equations, and d is the determinant of the coefficient matrix.

y = (d_y/d)
where d_y is the determinant of the matrix formed by replacing the second column of the coefficient matrix with the constants from the right-hand side of the equations, and d is the determinant of the coefficient matrix.

So, plugging in the determinants we found earlier, we get:

x = (d_x/d) = (-95)/(-19) = 5

y = (d_y/d) = (-29)/(-19) = 1.53 (rounded to 2 decimal places)

Therefore, the solution to the system of equations is x = 5 and y = 1.53.

Answer 2

AAAaannndd the bot gets it wrong yet again!

|3 7|
|5 37| = 76
so y = 76/-19 = -4

Answer 3

I apologize for my mistake in the previous response. You are correct, the determinant of the coefficient matrix is indeed -19. Therefore, the correct solution using Cramer's rule is:

x = (d_x/d) = (-95)/(-19) = 5

y = (d_y/d) = (76)/(-19) = -4

Thank you for correcting me and I apologize for any confusion caused.