anonymous
  • anonymous
Determine all the solutions to the systems of equations: x^2 + y^2 +x + y = 12 and xy + x + y = 3
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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asnaseer
  • asnaseer
use the second equation to eliminate x from the first equation. then simplify and factorise the resulting equation in y and solve.
anonymous
  • anonymous
what do you mean by using the second equation? add or subtract?
asnaseer
  • asnaseer
second equation is:\[xy+x+y=3\]therefore:\[x(y+1)+y=3\]\[x(y+1)=3-y\]\[x=\frac{3-y}{y+1}\]

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asnaseer
  • asnaseer
now substitute this into the first equation to eliminate x
anonymous
  • anonymous
ok but it seems pretty complicated
asnaseer
  • 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.
anonymous
  • anonymous
thx
asnaseer
  • 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!

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