hal_stirrup
in a graph where a liner equation intercept another liner equation. why is the intersection make the two equation equal.
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hal_stirrup
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|dw:1346965908373:dw|
ifrah34
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because the two angles reflect eachother
asnaseer
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a linear equation can be expressed in the form:\[y=mx+c\]which you have correctly drawn as a straight line graph
hal_stirrup
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explain more please . thanks
asnaseer
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now think of two linear equations - these would represent, say:\[y=m_1x+c_1\]and:\[y=m_2x+c_2\]
hal_stirrup
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ok
asnaseer
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now, if these two lines intersect, then, at the point of intersection, the y-values of both must be equal - agreed?
hal_stirrup
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agreed .
asnaseer
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therefore, we can say:\[m_1x+c_1=m_2x+c_2\]at the point of intersection
asnaseer
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which is the same as saying:\[y=y\]
hal_stirrup
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because y=y thats grate . amazing . tell if we have quadratic equations |dw:1346967366273:dw|
asnaseer
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same applies for quads - except this time you will get two solutions for x instead of one that you got for the linear case
hal_stirrup
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|dw:1346967476493:dw|
asnaseer
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correct
hal_stirrup
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lets say
asnaseer
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and each of these, in theory could give you two different y values
hal_stirrup
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y1=x^2 +mx + c
and
y2=x^2 +mx + c
asnaseer
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quads are usually written as:\[y=a_1x^2+b_1x+c_1\]and:\[y=a_2x^2+b_2x+c_2\]
hal_stirrup
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ok
asnaseer
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so at the points of intersection we will have:\[a_1x^2+b_1x+c_1=a_2x^2+b_2x+c_2\]
asnaseer
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which leads to a quadratic equation in x - solve to get the two values for x where these curves intersect
asnaseer
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in general, we could have two curves defined by:\[y=f(x)\]and:\[y=g(x)\]
|dw:1346967756823:dw|
asnaseer
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|dw:1346967787868:dw|
hal_stirrup
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ya
asnaseer
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and, at each point of intersection, the y and x values on each curve are equal
asnaseer
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I hope I have explained it well enough for you - let me know if you require any more explanation
hal_stirrup
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have outdone yourself
hal_stirrup
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many thanks.
asnaseer
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thx - and you are welcome my friend! :)
hal_stirrup
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what is the highest think your done in maths??
asnaseer
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think == thing?
hal_stirrup
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ya sorry
asnaseer
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:) I have studied for a PhD in Aeronautical Engineering. but that was many years ago. I now teach maths as a hobby because I still enjoy it.
hal_stirrup
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WOW, thats great. can send you some of my question from time to time?
asnaseer
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I'm not sure what you mean by "send", but if you mean message me now and then if no one else is helping you - then yes, by all means do - I'll be glad to help out when I can.
hal_stirrup
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by that i meant , the message on the top left corner. thanks
asnaseer
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ok - thats fine.
hal_stirrup
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am going to do a lot of calculus. nice one
asnaseer
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but bear in mind that I may not always respond immediately because I also moderate this site so please don't think I'm ignoring you in those cases. :)
hal_stirrup
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thanks. I will be patient . :)
asnaseer
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gr8! speak to you later then...