Question

Using Cramer's rule, the solution to the system of equations:

3x - y = -1 and -3x + 5y = 13
Can be written in the form:
Dx, Dy
D D
What is the value of Dy?

Answer 1

The value of Dy calculated using Cramer's rule for the system of equations 3x - y = -1 and -3x + 5y = 13 is 36.

Step-by-step explanation:

Using Cramer's rule to solve the system of equations 3x - y = -1 and -3x + 5y = 13, you'll need to calculate the determinant of the matrix associated with the variables, as well as the determinant of matrices with the constants substituted in the appropriate columns. The value of Dy is the determinant of the matrix formed by replacing the coefficients of y with the constants from the right-hand side of the equations.

• The original matrix (D) is:
  | 3 -1 |
  |-3 5 |
• To find Dy, we replace the second column with the constants:
  | 3 -1 |
  |-3 13 |
• Now, calculate the determinant for Dy: Dy = (3)(13) - (-1)(-3) = 39 - 3 = 36.

Therefore, the value of Dy in the context of Cramer's rule for this system of equations is 36.