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Find an ordered pair that is a solution of the system
4 2 1
3 2 3
x y
x y
+ = -
- =
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need_help!
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What the..? Wait.
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4x+2y=-1
3x-2y=3
Hero
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1
Add the equations together and what do you get?
need_help!
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Hmm
need_help!
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How do I add them?
chris
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Combine all of the like terms. Since you know that 4x+2y=-1 and 3x-2y=3, you also know that 4x+2y + 3x -2y = -1 + 3
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so, x=2/7 ?
chris
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good work =)
chris
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now how do you get y when x=2/7?
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umm, i think you just substitute right? O.o
chris
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yep =) [just plug x=2/7 back into either equation]
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Yay! This is easy =D Thank youu.
chris
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No problem. Now the general way to solve these types of problems (systems of equations), is to solve for one variable first, and then substitute back into the other equation. To do this, you mus have a separate equation for each unknown variable - for example in this problem there are two equations and two unknowns.
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Yes I get it! But for example you have like:
4x+4y=-1
3x-2y=3
What do you do here? you can't cancel the 'y' or 'x' out
chris
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well, you actually can if you know a small trick.
chris
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if you know that 3x - 2y = 3, you can multiply both sides by the same number and the equation will still be true (equivalent)
chris
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in this case, I can multiply both sides by 2
chris
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so 2(3x -2y) = 2*3
chris
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2
6x - 4y = 6
chris
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Now you can cancel out all of the y's by adding the two equations
chris
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4x + 4y = 4
6x - 4y = 6
need_help!
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Aooh! *smart* :P :D
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I like it! Thanks a lot for the help.
chris
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No problem. There are other ways to solve these types of problems, but just ask here when you find a case where it's hard to find a way to cancel out =). good luck!
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btw, the ordered pairs are :
(0,-5/14) and (2/7,0) ?