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mixed questions (need help)


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#1 Dscott24

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Posted 12 March 2006 - 01:13 PM

Hi,
can someone please help me with this question.


1. Two sides of a rectangle have equations y=2x and 2y+x=5. Find, algebraically, the coordinates of the vertex of the rectangle formed by these sides.

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#2 Steve

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Posted 12 March 2006 - 01:17 PM

Make a sketch of what's going on. Do you know what the question is actually asking you?
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#3 Dscott24

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Posted 12 March 2006 - 01:21 PM

QUOTE(Steve @ Mar 12 2006, 01:17 PM) View Post

Make a sketch of what's going on. Do you know what the question is actually asking you?



I think i do, is it just the point where the two sides of the rectangle meet. Can you give me a hint on what im supposed to do?

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#4 Steve

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Posted 12 March 2006 - 01:31 PM

Well, if the lines intersect then you are looking for a point which lies on both the lines, i.e. solving the equation of the lines simultaneously.

Have a look at the new Straight Lines notes for more information.
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#5 Dscott24

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Posted 12 March 2006 - 01:43 PM

QUOTE(Steve @ Mar 12 2006, 01:31 PM) View Post

Well, if the lines intersect then you are looking for a point which lies on both the lines, i.e. solving the equation of the lines simultaneously.

Have a look at the new Straight Lines notes for more information.



Yeah i just tried that, although i didnt get the right answer. can you try it and tell me what u got?

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#6 Steve

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Posted 12 March 2006 - 01:48 PM

I got (1,2).
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#7 Dscott24

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Posted 12 March 2006 - 01:50 PM

QUOTE(Steve @ Mar 12 2006, 01:48 PM) View Post

I got (1,2).



Yeah thats the right answer, can you show me how you did it?

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#8 Steve

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Posted 12 March 2006 - 01:58 PM

Ok, you have:



\begin{align*}y&=2x &(1)\\
2y+x&=5 &(2)\end{align*}

So all you have to do is solve them simultaneously. There are lots of ways you can do this (all covered in the notes), but I did this:

From (1), 2y=4x (by multiplying through by 2), then substitute this into (2):



\begin{align*}2y+x&=5\\
4x+x&=5\\
5x&=5\\
x&=1\end{align*}

Then substitute this into either (1) or (2) to get the y-coordinate.
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