Determine all the solutions to the systems of equations: x^2 + y^2 +x + y = 12 and xy + x + y = 3

Question

asnaseer · Answer

use the second equation to eliminate x from the first equation.
then simplify and factorise the resulting equation in y and solve.

anonymous · Answer

what do you mean by using the second equation? add or subtract?

asnaseer · Answer

second equation is:$$xy+x+y=3$$therefore:$$x(y+1)+y=3$$$$x(y+1)=3-y$$$$x=\frac{3-y}{y+1}$$

asnaseer · Answer

now substitute this into the first equation to eliminate x

anonymous · Answer

ok but it seems pretty complicated

asnaseer · Answer

it will look complicated initially, but if you follow it through then you should find it simplifying.
when you first substitute this fractional expression for x into the first equation, you will get an expression with fractions in it. just multiply both sides of the equation with a suitable value to get rid of the fractions - then try and simplify.

anonymous · Answer

thx

asnaseer · Answer

yw - let me know if you get stuck and I'll try to assist
It's pretty late here now so I need to get some sleep, but good luck!