Another way of solving a linear system is to use the elimination
method. In the elimination method you either add or subtract the
equations to get an equation in one variable.
When the coefficients of one variable are opposites you add the
equations to eliminate a variable and when the coefficients of one
variable are equal you subtract the equations to eliminate a
variable.
Example:
We can eliminate the x-variable by addition of the two
equations.
The value of y can now be substituted into either of the
original equations to find the value of x
The solution of the linear system is (0, 2).
To avoid errors make sure that all like terms and equal signs
are in the same columns before beginning the elimination.
If you don't have equations where you can eliminate a variable
by addition or subtraction you directly you can begin by
multiplying one or both of the equations with a constant to obtain
an equivalent linear system where you can eliminate one of the
variables by addition or subtraction.
Example:
Begin by multiplying the first equation by -4 so that the
coefficients of y are opposites
Substitute x in either of the original equations to get the
value of y
The solution of the linear system is (2, 3)
Video lesson: Solve the linear system using the
elimination method
