Solve 4x+6y=32 and

3x+2y=12, using cramer rule

First, I'd divide the 1st equation by 2, giving 2x+3y=16. Then,

D =
|2 3|
|3 2| = -5
Dx =
|16 3|
|12 2| = -4
Dy =
|2 16|
|3 12| = -24

x = Dx/D = 4/5
y = Dy/D = 24/5

To solve the system of equations using Cramer's Rule, we need to find the values of x and y that satisfy both equations.

Cramer's Rule uses determinants to find the values of x and y. Let's break down the steps involved:

Step 1: Set up the determinant D
D represents the determinant of the coefficients of x and y in the system of equations.

D = |4 6|
|3 2|

Step 2: Find the determinant Dx
Dx represents the determinant obtained by replacing the coefficients of x with the constants in the system of equations.

Dx = |32 6|
|12 2|

Step 3: Find the determinant Dy
Dy represents the determinant obtained by replacing the coefficients of y with the constants in the system of equations.

Dy = |4 32|
|3 12|

Step 4: Calculate x and y
Using Cramer's Rule, we can now find the values of x and y:

x = Dx/D
y = Dy/D

x = Dx/D = det(Dx)/det(D) = |32 6| / |4 6|
|12 2| |3 2|

y = Dy/D = det(Dy)/det(D) = |4 32| / |4 6|
|3 12| |3 2|

Step 5: Evaluate the determinants
Now, let's calculate the determinants and find the values of x and y:

D = (4 * 2) - (3 * 6) = 8 - 18 = -10

Dx = (32 * 2) - (6 * 12) = 64 - 72 = -8

Dy = (4 * 12) - (32 * 3) = 48 - 96 = -48

Finally, substitute the determinants into the formulas for x and y:

x = Dx/D = -8 / -10 = 4/5

y = Dy/D = -48 / -10 = 24/5

Therefore, the solution to the system of equations is x = 4/5 and y = 24/5.