Question 919862
Substitute for xy in the second equation, and at least you can find a relationship between x and y.  Then try to work with this and what you believe to be the simpler equation....


2x^2+3y^2=84, does not look useful.




INSTEAD, DO THIS WAY:
Solve for x in terms of y from....
...
{{{x=(3y^2)/y}}}
-
{{{2(3y)^2+xy-84=0}}}
{{{2(3y)^2+3y^2-84=0}}}, includes substitution for xy.
{{{18y^2+3y^2=84}}}
{{{21y^2=84}}}
{{{y^2=4}}}
{{{highlight(y=-2)}}}  or {{{highlight(y=2)}}}.


Find each corresponding value for each y just found.
{{{x=3*(-2)^2/(-2)}}}
{{{highlight(x=-6)}}} when {{{highlight(y=-2)}}}
-
{{{x=3(2)^2/2}}}
{{{highlight(x=6)}}} when {{{highlight(y=2)}}}