Year 9 Interactive Maths - Second Edition

Elimination Method

Solve the equation thus obtained.  Then substitute the value found for the variable in one of the given equations and solve it for the other variable.  Write the solution as an ordered pair.

Example 2

Solve the following simultaneous equations by using the elimination method:

Solution:

Label the equations as follows:

Notice that 3y appears in the left-hand side of both equations.  Adding the left-hand side of (1) and (2), and then the right-hand sides, gives:

Note:

We have added equals to equals, and addition eliminates y.

Substituting x = 3 in (1) gives:

So, the solution is (3, 3).

Example 3

Solve the following simultaneous equations by using the elimination method:

Solution:

Label the equations as follows:

Subtracting (2) from (1) gives:

Substituting  y = 4 in (1) gives:

So, the solution is (5, 4).

Example 4

Solve the following simultaneous equations by using the elimination method:

Solution:

Label the equations as follows:

Multiplying (1) by 2 and (2) by 3 gives:

Subtracting (3) from (4) gives:

Substituting x = 2 in (1) gives:

So, the solution is (2, 3).           

Key Terms

elimination method, ordered pair