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lemonsplk lemonsplk
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12 years ago
6x-y=3
3x-5y= -39
(2, 9)

can't seem to figure out what makes it a system of equations. I know the answer is "yes" but how do I know that?
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wrote...
#1
12 years ago
A system of equations is a number of functions indicating different lines.  The solution is the point of intersection of those lines.

You can either find the actual point of intersection using Elimination, Substitution, or Reflexion.  Or you can plug a known point into both equations.

6 *2 - 9 = 12 - 9 = 3, so that point is on that line.
3 * 2 - 5 * 9 = 6 - 45 = -39, so that point is also on that line.

And since the point is on both lines, it's the point of intersection, or the solution to the system of equations.
wrote...
#2
12 years ago
Substitute 2 in for X  and  9 in for Y  in  BOTH  equations and
see if they BOTH  give TRUE statements.

These  do  so  (2 , 9)  is the CORRECT  solution

Let me know if want to learn a FAST way to work a sysytem.
My students look at the problem and in one step write down the answer

Mathcerely,                  Robert  Jones  "Teacher/Tutor of Fine Students"
Moved Florida to France June 2011 but still tutor world-wide (USA , UK ,
France , Checz Republic ...)   free   using Skype.    If you need me to explain
further or any other math problem just let me know how to get in touch.
*********     A PRESENT FOR YOU
Ask someone to write a number, say a five-digit number.
(Can be a 2-digit.....3-digit.....4-digit....ect..?
Suppose the number written is
57836
Now, without showing the asker, you write a number on
a sheet of paper and keep it folded. You have to write the
number by subtracting 2 from the above number and
adding 2 in front which will be....
257834
Next, ask the person to write another five-digit number
below his original number. Suppose he writes 37589.
So you now have...
57836
37589
Now you write a five-digit number below it in such a
way that each digit is 9 minus digit above. You now have...
57836
37589
62410
Ask the person to add one more 5-digit number. If he
adds 54732, you add below it 45267. Note that you decided
the number by subtracting each of his digit from 9.
Thus, you now have.....
57836
37589
62410
54732
45267
Next, ask him to add all the number and he gets 257834
Show him the number which you had written as an answer
to this addition earlier in the folded paper and surprise him.
wrote...
#3
12 years ago
Quote from: lemonsplk (12 years ago)
6x-y=3
3x-5y= -39
(2, 9)

can't seem to figure out what makes it a system of equations. I know the answer is "yes" but how do I know that?


When you plug in the numbers , the expression should make sense.
The pair of numbers will satisfy both equations.
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