**Question**

**Introduction**

Somebody
said, “Dear Algebra, please stop asking me about your

*x*. She is not coming back. Don’t ask me*y*!”
Here we have
here linear equations that appear to be more tricky than the usual fanfare. This is because the coefficients of the
unknowns

*x*and*y*are fractions. In school, students learn to solve these using the*method of substitution*and the*method of elimination*. They tend to prefer to do it by the former method, because psychologically it seems easier to accept. However, the latter matter is generally more effective and yields a shorter solution. This question is like a fly trap for those who prefer the method of substitution. You make either*x*or*y*the subject from one of the equations, and then substitute that into the other equation. This yields a complicated algebraic fractions within algebraic fractions. The more complicated your solution is, the higher chance there is for making careless mistakes. It is a good idea that students get out of their comfort zones and adopt a new skill. So how do we do it?**The smart tactic**

First, we
need to clear away the fractions by multiplying through with the LCM of the
denominators appearing in each equation. For the first equation, LCM(4, 8) = 8. Since
4 is a factor of 8, 8 is like a giant that absorbs the number 4. OK,
so we multiply the first equation through by
8. For the second equation, we
multiply every term by LCM (3, 2) = 6

**Solution**

**Remarks**

As you can
see, equations [3] and [4] both contain – 3

*y*and this can be eliminated via subtraction. So the value of*x*comes out easily. Now once*x*is known, one can find the*y*!
For another example of simultaneous equations, please refer
to this article.

H04. Look for
pattern(s)

H05. Work
backwards

H10. Simplify
the problem

H11. Solve part
of the problem

H13* Use
Equation / write a Mathematical Sentence

**Suitable Levels**

*****Lower Secondary Mathematics (Secondary 2)

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

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