Cambridge International Mathematics

164 Formulae and simultaneous equations (Chapter 7)

Many problems can be described mathematically by apair of linear equations, or two equations of the

form ax+by=c, wherexandyare the two variables or unknowns.

We have already seen an example of this in theDiscoveryon page 158.

Once the equations are formed, they can then be solved simultaneously and thus the original problem solved.

The following method is recommended:

Step 1: Decide on the two unknowns; call themxandy, say. Do not forget the units.

Step 2: Write downtwoequations connectingxandy.

Step 3: Solve the equations simultaneously.

Step 4: Check your solutions with the original data given.

Step 5: Give your answer in sentence form.

The form of the original equations will help you decide whether to use the substitution method, or the

elimination method.

Example 19 Self Tutor

Two numbers have a sum of 45 and a difference of 13. Find the numbers.

Letxandybe the unknown numbers, wherex>y.

Then x+y=45 ::::::(1) f‘sum’ means addg

and x¡y=13 ::::::(2) f‘difference’ means subtractg

) 2 x =58 fadding (1) and (2)g

) x=29 fdividing both sides by 2 g

Substituting into (1) gives: 29 +y=45

) y=16

The numbers are 29 and 16.

Check: (1) 29 + 16 = 45 X (2) 29 ¡16 = 13 X

Example 20 Self Tutor

Find the cost of each coconut and each banana.

Let each coconut costxcents and each banana costycents.

) 5 x+14y= 870 ::::::(1)

8 x+9y= 990 ::::::(2)

To eliminatex, we multiply (1) by 8 and (2) by¡ 5.

F PROBLEM SOLVING [2.6]

When solving problems

with simultaneous

equations we must find

two equations containing

two unknowns.

The units must be the

same on both sides of

each equation.

When shopping in Jamaica, coconuts and bananas cost me ,

and coconuts and bananas cost.

514 $870

8 9 $9 90

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Y:\HAESE\IGCSE01\IG01_07\164IGCSE01_07.CDR Monday, 15 September 2008 4:51:58 PM PETER