Question 833257

1.{{{2x + 3y = 13}}}
2.{{{2xy + 5y^2 - 4x^2 = 41}}}

From eq. 1, 
{{{2x=13-3y}}}
Substitute,
{{{2xy + 5y^2 - 4x^2 = 41}}}
{{{2xy + 5y^2 - (2x)^2 = 41}}}
{{{(13-3y)y+5y^2-(13-3y)^2=41}}}
{{{13y-3y^2+5y^2-(9y^2-78y+169)=41}}}
{{{(-3+5-9)y^2+(13+78)y-169=41}}}
{{{-7y^2+91y-210=0}}}
{{{y^2-13y+30=0}}}
{{{(y-3)(y-10)=0}}}
Two solutions:
{{{y-3=0}}}
{{{y=3}}}
Then from eq. 1,
{{{2x=13-3(3)}}}
{{{2x=13-9}}}
{{{2x=4}}}
{{{x=2}}}
.
.
.
{{{y-10=0}}}
{{{y=10}}}
{{{2x=13-3(10)}}}
{{{2x=13-30}}}
{{{x=-17/2}}}