Give me the equations and I'll show you......equations in two variables are a little easier than with larger systems......
4x-5e=18
3e+5x=4
Rearrange as
4x - 5e = 18
5x + 3e = 4 assuming "e" is a variable, we have the matrix , A =
[ 4 - 5
[ 5 3 ] we need to find the inverse of this matrix
We have the form
[ a b
c d ] the inverse is given by
1 / [ ad - bc ] [ d -b =
-c a ]
1 / [ 4*3 - (-5)*(5) ] [ 3 5 =
-5 4 ]
1 / [ 12 + 25] [ 3 5 =
-5 4 ]
1/[37] [ 3 5 =
-5 4 ]
[ 3/37 5/37
-5/37 4/7]
Call this matrix the inverse of A = A-1
And call the column matrix [ 18 = b
4]
And the solution for ( x, e) is given by
A-1 * b = [ 3/37 5/37 * [18 =
-5/37 4/37 ] 4]
( (3/37)*18 + (5/37)* 4, (-5/37)*(18) + (4/37)*(4) )
( 74/ 37, -74/ 37 ) =
(2, -2 ) = (x, e)
Obviously, this is more easily solved with either substitution, elimination [or with Cramer's Rule]