Tuesday, March 24, 2015

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).

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