Question 884396
A solution using Elimination does not seem possible; but substitution should work.


Solve either equation for either variable; and substitute the expression into the other equation.  Solve for the remaining variable for its value and solve then for the other variable's value.


{{{x+y=7xy}}}
{{{x-7xy=-y}}}
{{{x(1-7y)=-y}}}
{{{x(7y-1)=y}}}
{{{highlight_green(x=y/(7y-1))}}}
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The other equation:
{{{2x-3y+xy=0}}}
{{{2(y/(7y-1))+3y+(y/(7y-1))y=0}}}
{{{2y/(7y-1)+3y+y^2/(7y-1)=0}}}, then multiply left and right by 7y-1,
{{{2y+3y(7y-1)+y^2=0}}}
{{{2y+21y^2-3y+y^2=0}}}
{{{22y^2-y=0}}}
{{{y(22y-1)=0}}}
{{{y=0}}} OR {{{y=1/22}}}


Continue this for the corresponding values for x....
Use the green-highlighted formula.


You cannot completely separate the x from the y in both equations in order to use Elimination Method.