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How to use the elimination method to solve linear system:

  1. Either add or subtract the equations to get an equation in one variable.
    • When the coefficients of one variable are opposites (<-  ->):
      • add (+) the equations to eliminate a variable
    •  when the coefficients of one variable are equal (=)

      •   subtract (-) the equations to eliminate a variable.

Example

3y + 2x = 65y − 2x = 10

Eliminate the x-variable by addition of the two equations.

3y+2x=6
+5y−2x=10
=8y=16
y=2

The value of y can now be substituted into either of the original equations to find the value of x

3y+2x=6
3⋅2+2x=6
6+2x=6
x=0