



 
Marissa, If 2x  y is 5 and 3x + y is 9 then their sum must be 5 + (9) = 4. That is
or simplifying
which is
Thus
Substitute this value of x into the first equation, 2x  y = 5, to find y. This is an example of one of the techniques used to solve linear systems. It's call the Method of Elimination. It worked nicely here because one equation contained y and the other contained y so in their sum the yterms were eliminated. Sometimes you need to manipulate the equations first to make the elimination work. For example to solve
I would first multiply both sides of the second equation by 2 to obtain
In this case if you subtract the second equation from the first you have
or
and hence
Penny  


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