How to show that x = y ?? (2,3 marks)

I have done part i) And have the correct answer of
Pos a
x^2=y^2+4

Pos b

(x+0.95)^2 = (y+1.05)^2 + 4

I was wondering why would the real answer not be x= and y=
Why is it like the above answer, if the question says write down 2 equations in X an d Y?

I also don't know how to do the second part, and would be grateful, if you could go through it

Thank you!

Question bellow.

If I understand correctly; you're asking why it's okay to leave those equations in that form?

If so; it's simply that they didn't ask you to make y or x the subject (subject means make it x= ... or y= ... ); so as long as you have some equation relating x and y you've done what they've asked.

For the hence show; multiply the brackets in the second equation out and see if that helps you see what to do.

OK I think I now understand your question

It says, write down two equations "in x and y". An equation "in x and y" doesn't have to look like y=... or x=..., it just has to be an equation that includes the variables x and y.

If the question said, "write an equation with x/y as the subject" or "write an equation for x/y in terms of y/x" then you would be required to write equations of the form x/y=...

For part ii) expand your brackets for pos B to get $x^2+1.9x+0.9025=y^2+2.1y+1.1025+4$
Re arrange to $x^2-y^2+1.9x-2.1y-0.2=4$

For pos a, we can re arrange to have $x^2-y^2=4$

So we can now solve these simultaneously: $x^2-y^2+1.9x-2.1y-0.2=x^2-y^2$
Re arrange to get your $2.1y=1.9x-0.2$

I have done part i) And have the correct answer of
Pos a
x^2=y^2+4

Pos b

(x+0.95)^2 = (y+1.05)^2 + 4

Edit (thanks guys)

I don't know how to do the second part, and would be grateful, if you could go through it

Thank you!

Question bellow.

Oh ok thanks for that! I was just struggling to find what to sub I get it now! I'll remember to look out to sub numbers with letters

a

y.

Part (iii) is just a continuation of this - you need to square both sides and then sub in (x^2 - 4) for y^2. Tbh, part (ii) is actually somewhat redundant and just a stepping stone I guess to help you get to part (iii); you could get to the quadratic in one go.

Ha no worries

What are the answers on the mark scheme for iii)? I just want to see if I'm heading in the right direction.

I was wondering, why would you have to square both sides? Then sub?? Please explain why you said this.
Thanks!



Can all of the above show me how to get there?

Final answer
x=4.25
y= 3.75

Use the quadratic formula to get x. Then sub x back into your original equation and you have got y.

When i said square both sides, i meant squaring both sides of 2.1y = 1.9x - 0.2, so that you have 4.41y^2 which you can replace with 4.41(x^2-4). Alternatively, you can just solve to get y = (1.9x-0.2)/2.1, and then square this and sub into x^2 = y^2 + 4. Essentially its the same thing either way.

Use the quadratic formula to get x. Then sub x back into your original equation and you have got y.

Oh so I have to use quadratic equation on this?

x^2 +1.9x+0.9025

Because the question is asking me to form a quad equation in x ???

If you said this, then why would green say the bellow??
And you also haven't said WHY you square both sides? What in the question or what do you think in your head, that tells you to "square both sides"?

Once I get this then I will understand it fully

I was wondering, why would you have to square both sides? Then sub?? Please explain why you said this.
Thanks!

Can all of the above show me how to get there?

Final answer
x=4.25
y= 3.75

If you said this, then why would green say the bellow??
And you also haven't said WHY you square both sides? What in the question or what do you think in your head, that tells you to "square both sides"?

Once I get this then I will understand it fully

So you square both sides of 2.1y=1.9x-0.2.
This gives you $4.41y^2=3.61x^2-0.76x+0.04$
We know that $y^2=x^2-4$ so we sub that in to get:
$4.41x^2-17.64=3.61x^2-0.76x+0.04$
Rearrange to get: $0.8x^2+0.76x-17.68=0$
Use quadratic formula for your values of x. Sub your values of x into one of the equations to get your values of y