Hey there! Sign in to join this conversationNew here? Join for free
x Turn on thread page Beta
    • Thread Starter
    Offline

    0
    ReputationRep:
    Hi,

    I've been revising simultaneous equations for an up coming exam and for the most part had no problems, except for 2 examples (out of 40), which I just can't solve and can't figure out why/where I'm going wrong! The sheet only gives the final answers, with no solution. If anyone could show me the solution to these it'd be massively appreciated.

    First one:
    y=x+6
    x^2+y^2=50

    Second one:
    y=2x-2
    x^2-y=5

    These aren't any different to the others which I've done, which is why I'm so baffled as to why I can't solve them (it's the subsitution method I've been using). Again I'd greatly appreciate any help. Thanks.
    • Wiki Support Team
    Offline

    14
    ReputationRep:
    Wiki Support Team
    For your first equation, substitute y = x + 6 into the quadratic one, and you get x^2 + (x+6)^2 = 50. Solve for x, then plug it into the above equation to solve for y. (If you draw the line y = x + 6 and the circle x^2 + y^2 = 50, you'll see you get two answers at the points of intersection.) For the second one, substitute y = 2x - 2 to get x^2 - (2x - 2) = 5, and do the same.

    If you're still stuck, post your working.
    Offline

    16
    ReputationRep:
    I'll do the first one for you, than see if you can do the second one yourself.

     

x^2 + (x + 6)^2 = 50



x^2 + x^2 + 12x + 36 = 50



2x^2 + 12x - 14 = 0



x^2 + 6x - 7 = 0



(x + 7)(x - 1) = 0



x = -7 \ y = 1



x = 1 \ y = 7
    Offline

    0
    ReputationRep:
    for the first one, y^2 = (x+6)^2 ...work that out and plug it into the bottom equation

    for the second one, x^2 -(2x - 2) = 5
    Offline

    12
    ReputationRep:
    Now remember to solve for y, and note which x solution goes with which y solution...
    Offline

    0
    ReputationRep:
    What are the answers? I get x=1, y=7 and x=-7 and y=-1 for the first and x=3, y=4 and x=-1 and y=-4 for the second. I don't want to start explaining how to get the wrong answers, though So, is these the answers you should get?
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by samir12)
    I'll do the first one for you, than see if you can do the second one yourself.

     

x^2 + (x + 6)^2 = 50



x^2 + x^2 + 12x + 36 = 50



2x^2 + 12x - 14 = 0



x^2 + 6x - 7 = 0



(x + 7)(x - 1) = 0



x = -7 \ y = 1

x = 1 \ y = 7
    Ahhh! I was doing "x^2 + x^2 = x^4" not 2x^2. :o: Thank you so much.

    For the second I've been doing:
    x^2 -(2x - 2) = 5
    x^2 - 2x - 7 = 0

    Then, of course, I'm stuck. Which makes me think I'm making yet another glaringly obvious and silly mistake.

    Thanks for all the responses everyone, didn't expect so many so quick!

    (Original post by miglash)
    What are the answers? I get x=1, y=7 and x=-7 and y=-1 for the first and x=3, y=4 and x=-1 and y=-4 for the second. I don't want to start explaining how to get the wrong answers, though So, is these the answers you should get?
    Yep, they're correct.
    Offline

    16
    ReputationRep:
     



x^2 -(2x - 2) = 5



x^2 - 2x + 2 = 5

    remember there is a -1 in front of the brackets, so -1 * -2 = + 2
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by samir12)
     



x^2 -(2x - 2) = 5



x^2 - 2x + 2 = 5

    remember there is a -1 in front of the brackets, so -1 * -2 = + 2
    I knew it'd be something obvious like that. >.< Thanks. If my rep was worth any I'd give it.
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: July 20, 2009
Poll
Do I go to The Streets tomorrow night?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.