The solution of a twovariable twoequation system is to determine an ordered pair that makes these equations true at the same time. We will study some methods below:
Replacement method
Solution:
we determine the value of x in the 1st equation.
x = 4  y
 We replaced this value in the 2nd equation.
2 . (4  y) 3y = 3
 We solve the equation formed.
8  2y 3y = 3 5y = 5 => We multiply by 1 5y = 5

 We replaced the found value of y, in any of the equations, determining x.
x + y = 4 x = 4  1 x = 3 
 The system solution is the ordered pair (3, 1).
V = {(3, 1)}
Addition Method
Being U = , observe the following system solution by the addition method.
Solution:
We add member to member equations:
2x = 16
x = 8
We replaced the found value of x, in any of the equations, determining y:
x + y = 10
8 + y = 10
y = 10  8
y = 2
The system solution is the ordered pair (8, 2).
V = {(8, 2)}
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