<PRE><B>Question 1182622</B>
&lt;br&gt;
Tutor @MathLover1 will virtually always solve any system of two equations in two unknowns using substitution.  That is a valid method; but often there are much easier ways.&lt;br&gt;
A student with only a little bit of problem solving experience will see the first equation as a difference of squares and will see if that leads to an easy path to the solution.&lt;br&gt;
And it does, as shown in the solution by tutor @ikleyn.&lt;br&gt;
{{{25x^2-y^2=36}}} --&gt; {{{(5x+y)(5x-y)=36}}}&lt;br&gt;
But the other equation tells us {{{5x+y=2}}}&lt;br&gt;
so&lt;br&gt;
{{{2(5x-y)=36}}}
{{{5x-y=18}}}&lt;br&gt;
And now we have a system of two linear equation that is easily solved using elimination:&lt;br&gt;
{{{5x+y=2}}}
{{{5x-y=18}}}&lt;br&gt;
The lesson from this:&lt;br&gt;
Don&#39;t be stuck with one method for solving a particular type of problem.  Instead, look for clues in the given problem that could possibly lead to a much faster and easier solution to the problem.&lt;br&gt;
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