In details

Systems Resolution


The solution of a two-variable two-equation 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


y = 1

  • We replaced the found value of y, in any of the equations, determining x.

x + y = 4
x
+ 1 = 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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