Question 1119601
This approach was not yet rechecked carefully.....

First Equation,
{{{x^3+x^2y=20}}}
{{{x^2(x+y)=20}}}
{{{x+y=20/x^2}}}


Second Equation,
{{{xy^2+y^3=45}}}
{{{y^2(x+y)=45}}}
{{{x+y=45/y^2}}}


Two expressions for x+y are equal.
{{{20/x^2=45/y^2}}}

{{{y^2/x^2=9/4}}}

{{{y/x=0+- 3/2}}}



Assuming the PLUS form would work,

{{{x=2y/3}}}
Substitute this into the second equation:
{{{y^3+(2/3)y*y^2-45=0}}}

{{{y^3+(2/3)y^3=45}}}

{{{(5/3)y^3=45}}}

{{{y^3=45*(3/5)}}}

{{{y^3=(9*5*3)/5=9*3=3^3}}}

{{{highlight_green(y=3)}}}


Solution not yet been checked carefully