The system of equations representing the problem is

and we have
brown M&M's and
green M&M's in the cookie jar.
<h3>Formulating the equations</h3>
If we let
represent the number of brown M&M's and
the number of green M&M's, then, from the sentence
"...<em>A cookie jar contains 315 M&M's. There are only brown and green M&M's in the jar</em>..."
we can construct the algebraic equation

Also, from the sentence
"...<em>The number of green M&M's is 8 times that of the brown M&M's</em>..."
we can construct the algebraic equation

overall, we have the system of equations with unknowns
and 

<h3>Solving the system of equations</h3>
Adding the two equations, we get

Substituting this value for
into the relationship 

Therefore, we have
brown M&M's and
green M&M's
Learn more about word problems and systems of equations here brainly.com/question/14111058