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# (C1) Quadratic Simultaneous Equation watch

1. Hi, stuck on this question..

---------------

Solve the following pairs of simulatneous equations.

7y - x = 49

x^2 + y^2 - 2x - 4y = 0

--------------

I rearranged 7y - x = 49 to give

x = 7y - 49 and added it into x^2 + y^2 - 2x - 4y = 0

to give

50y^2 - 704y + 2499 = 0

Huge numbers so used the quadratic equation x = -b +- sqrt b^2 - 4ac all over 2a.. however the discriminant is < 0 therefore indication no real roots. Therefore the lines do not cross (when i use these calculations). However there IS an answer in the book x = 0 y = 7.. (only crosses once).. Have i done my calculations wrong or is there another angle to tackle this question
Thanks,
Sean
2. (50 * 49) - (704 * 7) + 2 499 = 21

It should = 0 but it doesn't which shows you have made a mistake somewhere subbing equation 1 into 2.
3. (Original post by Bleak Lemming)
Hi, stuck on this question..

---------------

Solve the following pairs of simulatneous equations.

7y - x = 49

x^2 + y^2 - 2x - 4y = 0

--------------

I rearranged 7y - x = 49 to give

x = 7y - 49 and added it into x^2 + y^2 - 2x - 4y = 0

to give

50y^2 - 704y + 2499 = 0

Huge numbers so used the quadratic equation x = -b +- sqrt b^2 - 4ac all over 2a.. however the discriminant is < 0 therefore indication no real roots. Therefore the lines do not cross (when i use these calculations). However there IS an answer in the book x = 0 y = 7.. (only crosses once).. Have i done my calculations wrong or is there another angle to tackle this question
Thanks,
Sean
Can you not complete the square on x^2 + y^2 - 2x - 4y = 0 to give this;

(x-1)^2 + (y-2)^2 = 5

This is an equation of a circle.
4. (Original post by Bleak Lemming)
Hi, stuck on this question..

---------------

Solve the following pairs of simulatneous equations.

7y - x = 49

x^2 + y^2 - 2x - 4y = 0

--------------

I rearranged 7y - x = 49 to give

x = 7y - 49 and added it into x^2 + y^2 - 2x - 4y = 0

to give

50y^2 - 704y + 2499 = 0

Huge numbers so used the quadratic equation x = -b +- sqrt b^2 - 4ac all over 2a.. however the discriminant is < 0 therefore indication no real roots. Therefore the lines do not cross (when i use these calculations). However there IS an answer in the book x = 0 y = 7.. (only crosses once).. Have i done my calculations wrong or is there another angle to tackle this question
Thanks,
Sean

I think you have got the question wrong. Please check your ORIGINAL question.
5. (Original post by steve2005)
I think you have got the question wrong. Please check your ORIGINAL question.
The equations as you've given them definitely have no real solution. You can check that your given solution of (0,7) does not satisfy them.

If the equations are actually

7y - x = 49
x^2 + y^2 - 2x - 7y = 0

then (0,7) is indeed a solution, but not a unique one (there is another real solution).

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