-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 Ax
[ 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 Ay
[-2 4 = (-2)(-7) - (4)(1) = 14 - 4 = 10
1 -7 ]
And x is given by Ax / A = 5/5 = 1
And y is given by Ay / A = 10/5 = 2