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 January 7th, 2017, 05:12 PM #1 Member   Joined: Jan 2017 From: US Posts: 94 Thanks: 5 Best Method to Solve this System of Equations? :) For this system of equations: x + y = 15 x (4%) + y (1%) = 15(2%) What method would be the proper method to go about solving? I believe the answer is (5, 10). I tried to go about this using the addition method, and I may have been doing it wrong, but I kept getting caught up when adding x + x(.4). Would that be 2.4x? The part I am confused about is lining up the actual equations to add them. This is how I was doing it (again, sorry if this looks like it makes no sense at all) x + y = 15 + .04x + .01y = .30 ____________________ 2.04x + 1.01y = 45 I am pretty new to learning this, (adding equations like this specifically) so please excuse my answer if that was totally wrong. Lol. Any help would be greatly appreciated! Last edited by skipjack; January 9th, 2017 at 07:17 AM.
 January 7th, 2017, 05:22 PM #2 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,593 Thanks: 937 Math Focus: Elementary mathematics and beyond x + y = 15 x (4%) + y (1%) = 15(2%) Try multiplying the second equation by 100. Thanks from Indigo28
January 7th, 2017, 05:34 PM   #3
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Joined: Jan 2017
From: US

Posts: 94
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Quote:
 Originally Posted by greg1313 x + y = 15 x (4%) + y (1%) = 15(2%) Try multiplying the second equation by 100.
So if I multiply .04x + .01y by 100, I get 4x + 1y = 30.

And then the answer to that is also (5,10)...

So, are you saying to use the second equation multiplied by 100 rather than the original one to add them?

So if I added them,

x + y = 15
+ 4x + 1y = 30
_________________
5x + 3y = 45

Is that what you meant?

 January 7th, 2017, 05:38 PM #4 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,593 Thanks: 937 Math Focus: Elementary mathematics and beyond x + y = 15 4x + y = 30 Think! What if you subtract them? Thanks from Indigo28
 January 7th, 2017, 05:46 PM #5 Member   Joined: Jan 2017 From: US Posts: 94 Thanks: 5 Ooooohhhh ok, gotcha. I really am new enough to this, that I did not even know subtracting them was an option. So: 4x + 1y = 30 - x + y = 15 ______________ 3x = 15 x=5 5 + y = 15 5(4%) + y (1%) = 15(2%) 5 + 10 = 15 5(4%)+ 10(1%) = .30 So x= 5 and y= 10. Thank you! Thanks from greg1313
 January 7th, 2017, 06:08 PM #6 Global Moderator   Joined: Dec 2006 Posts: 18,048 Thanks: 1395 To preserve spacing, you can enclose text between [code] and [/code] as shown below. Code:  4x + 1y = 30 - x + y = 15 ___________ 3x = 15 Thanks from Indigo28
January 7th, 2017, 06:24 PM   #7
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Joined: Jan 2017
From: US

Posts: 94
Thanks: 5

Quote:
 Originally Posted by skipjack To preserve spacing, you can enclose text between [code] and [/code] as shown below. Code:  4x + 1y = 30 - x + y = 15 ___________ 3x = 15
Thanks skipjack! I didn't know that so I will definitely do it in the future!

 January 8th, 2017, 06:57 AM #8 Newbie   Joined: Jan 2017 From: Georgia Posts: 10 Thanks: 3 Try to only get one variable by using substitution or elimination. Here's a link that might help: https://www.khanacademy.org/math/alg...s-of-equations Thanks from Indigo28
 January 9th, 2017, 02:35 AM #9 Member   Joined: Sep 2016 From: India Posts: 88 Thanks: 30 Write both equations $x+y=15......(1)$ $0.04x+0.01y=0.30.....(2)$ Multiplying equation(1) by $0.04$ we get $0.04x+0.04y=0.60.....(3)$ Now, subtracting equation(2) from equation(3) we get $0.03y=0.30$ $y=10$ Putting value of $y$ in equation(1) we get $x+10=15$ $x=5$ Hence, $x=5,\;\;\;\;\;\;\; y=10$ Thanks from Indigo28

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