| To solve the simultaneous
equations, make the coefficients
of one of the variables the same value in both equations. Then
either add the equations or subtract one equation from the other
(whichever is appropriate) to form a new equation that contains only one
variable. This is referred to as eliminating the variable.
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 |
