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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