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 January 6th, 2017, 08:15 PM #1 Senior Member   Joined: Jan 2017 From: US Posts: 111 Thanks: 6 Which Method Should I use to Solve this System of Equations? x + y = 4 y = 3x I am not sure which method I should use for this system of equations. I could use the addition method, but there are't any numbers aside from 4 in the first equation, and the same would happen when using the elimination method, so how would that work? I can use either the addition method, the elimination method, the substitution method or the graphing method. Just looking at this, I have determined the ordered pair (1,3) to be the solution, but that is without using a particular "method" which is what I am supposed to do. Any help would be appreciated! Thanks Last edited by Indigo28; January 6th, 2017 at 08:22 PM.
 January 6th, 2017, 08:26 PM #2 Senior Member   Joined: Feb 2016 From: Australia Posts: 1,597 Thanks: 546 Math Focus: Yet to find out. Substitution looks easiest, but maybe you solved it intuitively, without really thinking about which method you used This can be a good sign of your understanding! It's given that y = 3x in the second equation, so just substitute your expression for y in the first equation; x + 3x = 4 4x = 4 x = 1. Now you know what x is, substitute it back into the second equation! y = 3(1) = 3. Looks to me like your answer is correct. Thanks from Indigo28
January 6th, 2017, 08:30 PM   #3
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 Originally Posted by Joppy Substitution looks easiest, but maybe you solved it intuitively, without really thinking about which method you used This can be a good sign of your understanding! It's given that y = 3x in the second equation, so just substitute your expression for y in the first equation; x + 3x = 4 4x = 4 x = 1. Now you know what x is, substitute it back into the second equation! y = 3(1) = 3. Looks to me like your answer is correct.

Wow that looks a lot more simple than I made it out to be lol. Thank you!

January 6th, 2017, 08:32 PM   #4
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 Originally Posted by Indigo28 Wow that looks a lot more simple than I made it out to be lol. Thank you!
No worries! Don't feel like it was a waste of time to do it another way that may have taken longer. It all counts

 January 7th, 2017, 04:36 AM #5 Global Moderator   Joined: Dec 2006 Posts: 19,045 Thanks: 1618 x + y = 4 3x - y = 0 Adding those eliminates y, giving 4x = 4, so x = 1. It's now possible to find y by substituting 1 for x in either equation. Alternatively, multiplying the first equation by 3 gives 3x + 3y = 12. Subtracting the second equation from that gives 4y = 12, so y =3. Thanks from Indigo28

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