# Problems leading to simultaneous equations

**Solving problems**

There maybe situations where a mathematical problem is given and the solution can be found by creating simultaneous equations. In these situations, the following factors should be considered:

a. Decide which letters to use to represent the unknown values.

b. Using the information provided, write down two equations.

c. Solve the simultaneous equations.

d. Check the values by substituting them back.

For example:

The sum of two numbers is 58 and the difference between the two numbers is 20. What are the two numbers?

Using the information provided, write a pair of simultaneous equations in terms of *a* and *b*,

*a* + *b* = 58

*a* – *b* = 20

Add the equations:

2*a* = 78

*a* = 39

To find *b*, substitute 39 in place of *a* in the first equation:

*a* + *b* = 58

39 + *b *= 58

*b* = 19

Check the solutions by substituting them into the other equation:

*a* – *b* = 20

39 – 19 = 20