The first step is to choose one of the two equation solve it for one of its variables. In doing this, one side ends up having one variable with no co-efficient, and the other side contains everything else that was moved.
  • First equation : x + 2y = 2
  • First step - Solve for variable : x = - 2y + 2
The second step is to plug-in the result into the corresponding variable in the other equation. For example, if you solved for the x while solving one of the equations for a variable, the value received for x is to be plugged in instead of x in the other equation.
  • Result after solving for variable x : x = -2y + 2
  • Second equation : 7x - 3y = -20
  • Second step - Plug in result : 7 ( -2y + 2 ) -3y = -20

  • Solve for y :
    7 ( -2y + 2 ) -3y = -20
    -14y +14 - 3y = -20
    -14y -3y = -20 - 14
    -17y = -34
    y = ( -34 ) / ( -17 )
    y = 2
The third step is to plug in the result received for the variable into any of the two equations so that the value of the other variable can be obtained.
  • Value of y : y = 2
  • First equation : x + 2y = 2
  • Third step - Plug in result : x + 2 ( 2 ) = 2
  • Solve for x :
    x + 2 ( 2 ) = 2
    x + 4 = 2
    x = - 4 + 2
    x = -2
The problem has been solved. The x and y values are -2 and 2 respectively.


x = - 2 , y = 2

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