**Question**

**Introduction**

This is a
secondary 2 (» grade 8) problem that involves linear simultaneous equations in two
unknown. It looks non-linear and indeed
if you try to solve for

*x*and*y*directly, you might get into a big mess with extraneous solutions to boot. What should our approach be?**Observations**

It is
always a good idea to stare at the question for a little while longer before
jumping in to try to solve it. Let us (mentally)
reformat the equations a little bit.

Do you
notice any repeated chunks? Chunking is
very useful. Let use substitutions for
those chunks to simplify the equations.

**Solution**

**Final Remarks**

To
recap: It is a good learn to make observations first before attempt to solve the
problem. If you see any repeated chunks, it is a good idea to use
substitution to simplify the problem. Once the reciprocals have been substituted, we
try to use elimination (which is usually the more effective method). Also, try as far as possible to avoid
fractions. By multiplying equation [2]
by 5, we get – 30

For another example of simultaneous equations, please refer to thisarticle.

*Y*, which can be cancelled if we multiply 15*Y*by 2. Thus*Y*is eliminated. The problem becomes easy from this point onwards.For another example of simultaneous equations, please refer to thisarticle.

H04. Look for
pattern(s)

H09. Restate
the problem in another way

H10. Simplify
the problem

H11. Solve part
of the problem

H13* Use
Equation / write a Mathematical Sentence

**Suitable Levels**

*****Lower Secondary Mathematics (Secondary 1)

*****GCE ‘O’ Level “Elementary” Mathematics (revision)

* other syllabuses that involve algebra and
simultaneous linear equations

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