You may also consider the alternative method, that uses determinants, such that:

x-2y = 5

2x-y = 3

Form the determinant of the system such that:

=

You need to find the variable x such that:

You need to find the variable y such that:

Hence, evaluating the solutions to the system yields and .

x-2y = 5 .........(1)

2x - y = 3 .........(2)

To solve the system , we will use the elimination method:

multiply (1) by -2 and add to (2);

==>-2x + 4y = -10

==> 2x - y  = 3

==> 3y = -7

==> y= -7/3

==> x = 2y + 5

            = 2(-7/3) + 5 = -14/3 + 15/3 = 1/3

==> x = 1/3