Math CentralQuandaries & Queries


Question from Maryam, a student:

I looked at your example of simultaneous equations with fractions and applied it to my question from an educate exam papers but I couldn't get it to work. The question is:

x/8 - y = -5/2
3x + y/3 = 13

Hi Maryam,

I'm not sure what method you applied to this problem but I looked for a way to eliminate one of the variables. What I noticed is that if you multiply both sides of the second equation by 3 the term $y/3$ becomes $y$ and then if you add the two equations the $y$ term is eliminated. This method does work but I prefer to eliminate all the fractions so I would multiply both sides of the first equation by 8 and both sides of the second equation by 3 to get

x - 8y &=& -20\\
9x + y &=& 39.

If you now multiply both sides of the second equation by 8 you can eliminate the$ $y term.

x - 8y &=& -20\\
72x + 8y &=& 312.

Adding the two equations gives

\[73 x = 292.\]

Solve for $x$ and substitute into one of the equations to find $y.$


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