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January 7th, 2017, 06:12 PM   #1
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Question 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.
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January 7th, 2017, 06:22 PM   #2
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x + y = 15

x (4%) + y (1%) = 15(2%)

Try multiplying the second equation by 100.
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January 7th, 2017, 06:34 PM   #3
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Quote:
Originally Posted by greg1313 View Post
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
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5x + 3y = 45

Is that what you meant?
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January 7th, 2017, 06:38 PM   #4
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x + y = 15
4x + y = 30

Think! What if you subtract them?
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January 7th, 2017, 06:46 PM   #5
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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!
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January 7th, 2017, 07:08 PM   #6
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To preserve spacing, you can enclose text between [code] and [/code] as shown below.
Code:
  4x + 1y = 30
-  x +   y = 15
  ___________
  3x        = 15
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January 7th, 2017, 07:24 PM   #7
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Quote:
Originally Posted by skipjack View Post
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!
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January 8th, 2017, 07:57 AM   #8
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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
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January 9th, 2017, 03:35 AM   #9
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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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