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January 7th, 2017, 06:12 PM  #1 
Senior Member Joined: Jan 2017 From: US Posts: 104 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 08:17 AM. 
January 7th, 2017, 06:22 PM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,745 Thanks: 1001 Math Focus: Elementary mathematics and beyond 
x + y = 15 x (4%) + y (1%) = 15(2%) Try multiplying the second equation by 100. 
January 7th, 2017, 06:34 PM  #3  
Senior Member Joined: Jan 2017 From: US Posts: 104 Thanks: 5  Quote:
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, 06:38 PM  #4 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,745 Thanks: 1001 Math Focus: Elementary mathematics and beyond 
x + y = 15 4x + y = 30 Think! What if you subtract them? 
January 7th, 2017, 06:46 PM  #5 
Senior Member Joined: Jan 2017 From: US Posts: 104 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! 
January 7th, 2017, 07:08 PM  #6 
Global Moderator Joined: Dec 2006 Posts: 18,595 Thanks: 1493 
To preserve spacing, you can enclose text between [code] and [/code] as shown below. Code: 4x + 1y = 30  x + y = 15 ___________ 3x = 15 
January 7th, 2017, 07:24 PM  #7 
Senior Member Joined: Jan 2017 From: US Posts: 104 Thanks: 5  
January 8th, 2017, 07:57 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...sofequations 
January 9th, 2017, 03:35 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, $x=5,\;\;\;\;\;\;\; y=10$ 

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