What is -2a + 3b =4, a - 4b = -7 using Cramers rule

Solve the following system: USE CRAMER'S RULE
{3 b-2 a = 4
a-4 b = -7
Express the system in matrix form:
(-2 | 3
1 | -4)(a
b) = (4
-7)
Solve the system with Cramer's rule:
a = 4 | 3
-7 | -4/-2 | 3
1 | -4 and b = -2 | 4
1 | -7/-2 | 3
1 | -4
-2 | 3
1 | -4 = -2 (-4)-3×1 = 5:
a = 4 | 3
-7 | -4/5 and b = -2 | 4
1 | -7/5
4 | 3
-7 | -4 = -(3 (-7))+4 (-4) = 5:
a = 5/5 and b = -2 | 4
1 | -7/5
Cancel terms: 5/5 = 1:
a = 1 and b = -2 | 4
1 | -7/5
-2 | 4
1 | -7 = -2 (-7)-4×1 = 10:
a = 1 and b = 10/5
Divide 10 by 5: 10/5 = (2×5)/(1×5) = 2:
Answer: |a = 1        and           b = 2

-2a + 3b =4 

  a - 4b = -7

Take the determinant of the coefficient matrix  [we'll call this "A" ]

[ -2   3          =         (-2)(-4) - (3)(1)   =  8 - 3  = 5

 1   -4 ]  

Substitute the answer column into the first column of the previous matrix and take the determinant.....call this A_x 

[ 4   3       =   4(-4) - (-7)(3)   =  -16+ 21  =  5

 -7   -4]

Now......substitute the answer column into the second column of the first matrix and take the determinant .....call this A_y

[-2  4     =     (-2)(-7) - (4)(1)  =  14 - 4  = 10

 1  -7 ]

And x is given by  A_x / A   = 5/5  = 1

And y is given by A_y / A = 10/5  = 2