Simultaneous equation question

  • Context: High School 
  • Thread starter Thread starter james_rich
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Discussion Overview

The discussion revolves around solving a system of simultaneous equations involving a linear equation and a quadratic equation. Participants are checking the correctness of their solutions and addressing potential mistakes in the factorization process.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant presents their solution to the equations y = 2 - x and x² + 2xy = 3, claiming to find the coordinates (-1, 3) and (3, -1).
  • Another participant points out a mistake in the factorization, suggesting that x = 1 should be a solution instead of x = -1.
  • A participant expresses confusion about the highlighted mistake and requests further clarification.
  • A later reply confirms that x = 3 is correct but acknowledges that the correct value for x should be 1, leading to the coordinates (-1, 3) and (1, 1).
  • One participant offers advice on factorization, suggesting that having a positive coefficient for x² can be helpful.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the initial solution, as there are conflicting views on the correct values of x. The discussion reflects multiple competing interpretations of the factorization process and its outcomes.

Contextual Notes

There are unresolved issues regarding the factorization steps and the implications of sign changes in the solutions. The discussion highlights the importance of careful attention to detail in mathematical reasoning.

james_rich
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Hey just need my answer to be checked on this problem
just to clarify x2 means x squared!

Solve the following

y = 2 - x
x2 + 2xy = 3

Substitute equations

x2 + 2x(2 - x) = 3
x2 + 4x - 2 x2 = 3
-x2 + 4x - 3 = 0

Factorising

(-x + 1) (x - 3) = 0

so x = -1 and 3
_____________________________________________

as y = 2 - x

y = 2 - 3
= -1

y = 2 + 1
= 3

so the co ordinates for the two roots of this curve will be

(-1, 3) and (3, -1)

is this the right answer? i believe it to be, but my answer books says differently!

Please check my answer.
Thanx in advance!
 
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james_rich said:
Hey just need my answer to be checked on this problem
just to clarify x2 means x squared!
Solve the following
y = 2 - x
x2 + 2xy = 3
Substitute equations
x2 + 2x(2 - x) = 3
x2 + 4x - 2 x2 = 3
-x2 + 4x - 3 = 0
Factorising
(-x + 1) (x - 3) = 0
so x = -1 and 3

_____________________________________________
as y = 2 - x
y = 2 - 3
= -1
y = 2 + 1
= 3
so the co ordinates for the two roots of this curve will be
(-1, 3) and (3, -1)
is this the right answer? i believe it to be, but my answer books says differently!
Please check my answer.
Thanx in advance!

You made a small mistake where I highlighted.
 
sorry, i still don't understand, i checked what i did, i can't see what's wrong with the bit highlighted!

Can anyone elaborate?
 
james_rich said:
sorry, i still don't understand, i checked what i did, i can't see what's wrong with the bit highlighted!
Can anyone elaborate?
I didn't read it all but if your factorization was correct, then x = 1 is a solution and not x = -1.
 
i think i see what i have done wrong

the x = 3 is right

but it is -x = -1!

so x = 1

so to start again...

as y = 2 - x
y = 2 - 3
= -1
y = 2 - 1
= 1
so the co ordinates for the two roots of this curve is
(-1, 3) and (1, 1)

Thanx a lot, this is the answer in the book, easy mistake i made i think! bah humbug with the positive and negative signs!

Cheers! I can sleep now!
 
Good :smile:
 
A word of advice, when you factorise like that it usually helps to have the x^2 coefficient be positive.
 

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