Sometime we are given more than one equation (in Russian this is called a “system of equations”.

This additional information let’s us find out the value of more than one unknown (or letter). In general, provided that all of the equations are genuinely different, we can find out as many unknowns as we have equations.

There are two methods that we can use to solve simultaneous equations. We need to be comfortable using both, as depending on the specifics of the question, one method will normally be much quicker and easier than the other.

The two methods are:

• Elimination of a variable; and
• Substitution.

Examples

Let’s try some of these on the board at the front after the teacher has done some to show us the method:

Exercise

Let’s complete the exercise 8F on page 119 of the textbook. Note that this exercise has been set up so that mostly you are practicing elimination. But don’t forget that the substitution method is also important and often very helpful.

Below are the answers for this exercise: