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January 6th, 2017, 09:15 PM   #1
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Cool 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!

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Last edited by Indigo28; January 6th, 2017 at 09:22 PM.
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January 6th, 2017, 09:26 PM   #2
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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.
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January 6th, 2017, 09:30 PM   #3
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Quote:
Originally Posted by Joppy View Post
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!
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January 6th, 2017, 09:32 PM   #4
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Quote:
Originally Posted by Indigo28 View Post
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
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January 7th, 2017, 05:36 AM   #5
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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.
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