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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

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  1. asnaseer
    • 4 years ago
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    use the second equation to eliminate x from the first equation. then simplify and factorise the resulting equation in y and solve.

  2. anonymous
    • 4 years ago
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    what do you mean by using the second equation? add or subtract?

  3. asnaseer
    • 4 years ago
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    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
    • 4 years ago
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    now substitute this into the first equation to eliminate x

  5. anonymous
    • 4 years ago
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    ok but it seems pretty complicated

  6. asnaseer
    • 4 years ago
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    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
    • 4 years ago
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    thx

  8. asnaseer
    • 4 years ago
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    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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