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Qudratic simultaneous equations

The question is:
y = x + 2
y = x squared - 4

I don't want to use the elimination method, that is not allowed but I need help.
How do I do this?
y = x + 2 (1)
and
y = x^2 - 4 (2)

Sub 1 into 2.

Solve from there.
Reply 2
Original post by Bulletzone
y = x + 2 (1)
and
y = x^2 - 4 (2)

Sub 1 into 2.

Solve from there.


so you mean? x + 2 = x^2 - 4

Sorry if I'm making you frustrated, by my lack of knowledge. I got moved up to a top set recently, and am now doing higher tier work, but I haven't been taught it, so I feel once I'm taught a method I'll get it, I'm a year 10 btw.
Reply 3
Original post by Cod3tte
so you mean? x + 2 = x^2 - 4

Sorry if I'm making you frustrated, by my lack of knowledge. I got moved up to a top set recently, and am now doing higher tier work, but I haven't been taught it, so I feel once I'm taught a method I'll get it, I'm a year 10 btw.


yeah, rearrange to equal 0 and then solve the quadratic, x^2-x-6=0
Original post by Cod3tte
so you mean? x 2 = x^2 - 4

Sorry if I'm making you frustrated, by my lack of knowledge. I got moved up to a top set recently, and am now doing higher tier work, but I haven't been taught it, so I feel once I'm taught a method I'll get it, I'm a year 10 btw.


Yes that’s right 😊

X 2 = x^2 -4

Rearrange to make it all equal 0

X^2 - x - 6 = 0

Put these into brackets

(X - 3) (x 2) = 0

Make each bracket equal 0 separately

(X-3)=0 and (x 2)=0

Solve for x

X-3=0 so x=3 and x 2=0 so x also equals -2

Final answers are:
X=3, x= -2

EDIT: I factorised wrong!!
(edited 5 years ago)
Original post by NMauger96
Yes that’s right 😊

X + 2 = x^2 -4

Rearrange to make it all equal 0

X^2 - x - 6 = 0

Put these into brackets

(X - 6) (x + 1) = 0

Make each bracket equal 0 separately

(X-6)=0 and (x+1)=0

Solve for x

X-6=0 so x=6 and x+1=0 so x also equals -1

Final answers are:
X=6, x= -1


I know I’ve given you the answer but I hope I’ve explained it to allow you to understand how to work out further questions 😊
Reply 6
Original post by NMauger96

X^2 - x - 6 = 0

Put these into brackets

(X - 6) (x + 1) = 0


You didn't factorise correctly.
Original post by NMauger96
Yes that’s right 😊

X + 2 = x^2 -4

Rearrange to make it all equal 0

X^2 - x - 6 = 0

Put these into brackets

(X - 6) (x + 1) = 0

Make each bracket equal 0 separately

(X-6)=0 and (x+1)=0

Solve for x

X-6=0 so x=6 and x+1=0 so x also equals -1

X=6, x= -1


Your quadratic should be (x-3)(x+2)

The quadratic with roots that you have obtained would yield you x^2 - 5x - 6, not x^2 - x - 6, as required.
Original post by Cod3tte
so you mean? x + 2 = x^2 - 4

Sorry if I'm making you frustrated, by my lack of knowledge. I got moved up to a top set recently, and am now doing higher tier work, but I haven't been taught it, so I feel once I'm taught a method I'll get it, I'm a year 10 btw.


Hey, Don't worry about it nobody understands something on first glance.

so this is what we were told:

y=x+5y= x + 5
and
y=x24y = x^{2} - 4

A simultaneous equation just means that there is a number that is true for both of the equations.
e.g.

y=x+5 y = x + 5
y=9x y = 9 - x

Looking at these equations, What must x be to make them both true?
It must be 2.
The substitution method allows us to make both equations equal one another as that is essentially what a Simultaneous equation is.

so
Let's call y=x+5 y = x + 5 equation (1) and y=9x y = 9 - x equation (2).
Remember: Both equations equal one another.

so we can say that both Y's are the same therefore 9x=x+5 9- x = x + 5 therefore 2x=4 2x = 4 so x=2 x = 2.

We can do the same thing for your question, Substitute one y into the other and re-arrange to get a quadratic and solve.

Feel free to ask any other questions.
Reply 9
Original post by AryanGh
Your quadratic should be (x-3)(x+2)

The quadratic with roots that you have obtained would yield you x^2 - 5x - 6, not x^2 - x - 6, as required.


In that case I've got it right, thats what I got.
OP.

You're on the right track so far, what you need to do is equate your two expressions for y.

So x^2 - 4 = x + 2

Now, bring these all to one side x^2 - x - 6 = 0

Now, you can either factorise in your head, or if you're really not sure, use the quadratic formula,

With your values of x, substitute them into an expression of y and see what you get!
Original post by AryanGh
Your quadratic should be (x-3)(x+2)

The quadratic with roots that you have obtained would yield you x^2 - 5x - 6, not x^2 - x - 6, as required.


That’s very true! Thank you!! It’s been about 4years since I did quadratics

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