## anonymous 4 years ago Determine all the solutions to the systems of equations: x^2 + y^2 +x + y = 12 and xy + x + y = 3

1. asnaseer

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

2. anonymous

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

3. asnaseer

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

4. asnaseer

now substitute this into the first equation to eliminate x

5. anonymous

ok but it seems pretty complicated

6. asnaseer

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.

7. anonymous

thx

8. asnaseer

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!