we should write the given equation in matrix form
[ 4 -3 ] [ x ] [ 7 ]
=
[ 1 5 ] [ y ] [ 13 ]
Next find inverse of the matrix which is i.e ___1_______ x [ 5 3 ]
(4*5 -- (1 *(-3)) [ -1 4 ]
inverse of the equation is __1__ x [ 5 3 ] = [ 5/23 3/23 ]
23 [-1 4 ] [ -1/23 4/23 ]
then multiply the inverse value on both sides of the equation
[5/23 3/23 ] [ 4 -3 ] [ x ] [5/23 3/23] [7 ]
=
[-1/23 4/23] [ 1 5 ] [ y ] [-1/23 4/23] [13 ]
multiply by matrix method
[20/23 +3/23 -15/23 +15/23 ] [ x ] [ 35/23+39/23 ]
=
[ -4/23+4/23 3/23+20/23 ] [ y ] [-7/23+52/23 ]
[ 1 0 ] [ x ] [ 74/23 ]
=
[ 0 1 ] [ y ] [ 45/23 ]
[ x ] [ 74/23 ]
=
[ y ] [ 45/23 ]
is the coefficient matrix
