solve the sustem : 2x + y = 3 3y - 2x = 2

We'll re-write the equations:

2x +
y = 3

-2x + 3y = 2

We'll use the matrix
to solve the system. We'll form the matrix of the system, using the coefficients of x and
y:

        [2        1]

A
=

        [-2       3]

We'll calculate
the determinant of the system:

detA = 6 + 2 =
8

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

x = det
X/detA

             |3       1|

det
X =

             |2       3|

detX =9
- 2 = 7

x = det X/detA

x
= 7/8

We'll calculate
y:

           |2       
3|

det Y =

           |-2      
2|

det Y = 4 + 6

det Y =
10

y = detY/detA

y =
10/8

y =
5/4

The solution of the system is: (7/8
, 5/4).