## hal_stirrup 3 years ago in a graph where a liner equation intercept another liner equation. why is the intersection make the two equation equal.

1. hal_stirrup

|dw:1346965908373:dw|

2. ifrah34

because the two angles reflect eachother

3. asnaseer

a linear equation can be expressed in the form:\[y=mx+c\]which you have correctly drawn as a straight line graph

4. hal_stirrup

5. asnaseer

now think of two linear equations - these would represent, say:\[y=m_1x+c_1\]and:\[y=m_2x+c_2\]

6. hal_stirrup

ok

7. asnaseer

now, if these two lines intersect, then, at the point of intersection, the y-values of both must be equal - agreed?

8. hal_stirrup

agreed .

9. asnaseer

therefore, we can say:\[m_1x+c_1=m_2x+c_2\]at the point of intersection

10. asnaseer

which is the same as saying:\[y=y\]

11. hal_stirrup

because y=y thats grate . amazing . tell if we have quadratic equations |dw:1346967366273:dw|

12. asnaseer

same applies for quads - except this time you will get two solutions for x instead of one that you got for the linear case

13. hal_stirrup

|dw:1346967476493:dw|

14. asnaseer

correct

15. hal_stirrup

lets say

16. asnaseer

and each of these, in theory could give you two different y values

17. hal_stirrup

y1=x^2 +mx + c and y2=x^2 +mx + c

18. asnaseer

19. hal_stirrup

ok

20. asnaseer

so at the points of intersection we will have:\[a_1x^2+b_1x+c_1=a_2x^2+b_2x+c_2\]

21. asnaseer

which leads to a quadratic equation in x - solve to get the two values for x where these curves intersect

22. asnaseer

in general, we could have two curves defined by:\[y=f(x)\]and:\[y=g(x)\] |dw:1346967756823:dw|

23. asnaseer

|dw:1346967787868:dw|

24. hal_stirrup

ya

25. asnaseer

and, at each point of intersection, the y and x values on each curve are equal

26. asnaseer

I hope I have explained it well enough for you - let me know if you require any more explanation

27. hal_stirrup

have outdone yourself

28. hal_stirrup

many thanks.

29. asnaseer

thx - and you are welcome my friend! :)

30. hal_stirrup

what is the highest think your done in maths??

31. asnaseer

think == thing?

32. hal_stirrup

ya sorry

33. asnaseer

:) 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.

34. hal_stirrup

WOW, thats great. can send you some of my question from time to time?

35. asnaseer

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.

36. hal_stirrup

by that i meant , the message on the top left corner. thanks

37. asnaseer

ok - thats fine.

38. hal_stirrup

am going to do a lot of calculus. nice one

39. asnaseer

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. :)

40. hal_stirrup

thanks. I will be patient . :)

41. asnaseer

gr8! speak to you later then...

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