Cramer's rule
I understand the method but idk how to do this question
6x+2y=-44
-7+9Y=-96
To solve the given system of equations using Cramer's Rule, you need to find the values of x and y.
Cramer's Rule states that for a system of linear equations in the form of:
ax + by = e
cx + dy = f
The values of x and y can be found using the following formulas:
x = Dx/D
y = Dy/D
where:
D = determinant of the coefficient matrix
Dx = determinant of the matrix formed by replacing the x-values in the coefficient matrix with the constant terms
Dy = determinant of the matrix formed by replacing the y-values in the coefficient matrix with the constant terms
Let's solve the given system of equations step by step:
The given system of equations is:
6x + 2y = -44 --(1)
-7x + 9y = -96 --(2)
Step 1: Create the coefficient matrix (A).
The coefficient matrix (A) is formed by taking the coefficients of x and y in the same order as the equations:
A = | 6 2 |
| -7 9 |
Step 2: Calculate the determinant of the coefficient matrix (D).
D = (6 * 9) - (2 * -7)
D = 54 + 14
D = 68
Step 3: Calculate the determinant of the matrix formed by replacing the x-values in the coefficient matrix with the constant terms (Dx).
Dx = (-44 * 9) - (2 * -96)
Dx = -396 + 192
Dx = -204
Step 4: Calculate the determinant of the matrix formed by replacing the y-values in the coefficient matrix with the constant terms (Dy).
Dy = (6 * -96) - (-44 * -7)
Dy = -576 + 308
Dy = -268
Step 5: Calculate the values of x and y using Cramer's Rule.
x = Dx/D
x = -204/68
x = -3
y = Dy/D
y = -268/68
y = -3.94 (rounded to two decimal places)
Therefore, the solution to the system of equations is:
x = -3
y = -3.94