x+y=5 2x-y=1 find x and y values

We'll use the matrix to solve the system. We'll form the
matrix of the system:

        1       
1

A =

        2      
-1

We'll calculate the determinant of the
system:

detA = -1 - 2 =
-3

Since det A is not cancelling, the system is
determinated and it will have only one solution.

x = det
X/detA

             5       
1

det X =

             1      
-1

detX = -5 - 1 = -6

x = det
X/detA

x =
-6/-3

x =
2

We'll calculate
y:

           1       
5

det Y =

           2      
1

det Y = 1 - 10

det Y =
-9

y = detY/detA

y =
-9/-3

y =
3

The solution of the system
is: (2 , 3).