The Algebraic Methods

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The Algebraic Methods

Use of algebra enables us to obtain exact answers to simultaneous equations. There are two algebraic methods, the Substitution Method and the Elimination Method.

Substitution Method

To solve the simultaneous equations, find the value of y in terms of x (or vice versa) for one of the two equations and then substitute this value into the other equation.

Example 2

Solve the following simultaneous equations by using the substitution method:

Solution:

Label the equations as follows:

x + x + 3 = 15 so we find x = 6

So, the solution is (6, 9).

Note:

It is convenient to use the substitution method when one of the given equations has one of the variables as its subject.

Example 3

Solve the following simultaneous equations by using the substitution method:

Solution:

Label the equations as follows:

2(2y + 10) + y = 5, so we find y = -3

Substituting y = -3 in (1) gives x = 2(-3) + 10 = 4

Key Terms

algebraic methods, substitution method

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