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Variables Equations

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Variables Equations

by phoenix9801 » Fri Jun 04, 2010 10:31 am
1-

9(-27x-21) = 54 -27y


2-

9(18-24x) = 162 +54y




Please Help, Thanks

Please explain step-by-step instructions (detials)

P.S for some reason I am unable to obtain the same answer for number 1 which is (y=9x-9) and for number 2 which is (y=4x)
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by Rich@VeritasPrep » Fri Jun 04, 2010 10:57 am
Hey there,

If you work through the problem, you'll find that the answer to (1) is actually y=9x+9 and the answer to (2) is y=-4x. Here's why:

1.

9(-27x - 21) = 54 - 27y

9*3(-9x - 7) = 9*3(2 - y)

-9x - 7 = 2 - y

9x + 7 = y - 2 (multiply the above equation by -1)

y = 9x + 9


2-

9(18-24x) = 162 +54y

9*6(3 - 4x) = 54(3 + y)

3 - 4x = 3 + y

-4x = y

Let me know if you need clarification for any of these steps!
Rich Zwelling
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by phoenix9801 » Fri Jun 04, 2010 11:15 am
raz1024 wrote:Hey there,

If you work through the problem, you'll find that the answer to (1) is actually y=9x+9 and the answer to (2) is y=-4x. Here's why:

1.

9(-27x - 21) = 54 - 27y

9*3(-9x - 7) = 9*3(2 - y)

-9x - 7 = 2 - y

9x + 7 = y - 2 (multiply the above equation by -1)

y = 9x + 9


2-

9(18-24x) = 162 +54y

9*6(3 - 4x) = 54(3 + y)

3 - 4x = 3 + y

-4x = y

Let me know if you need clarification for any of these steps!


Thanks for the clarification, But I am not so sure about number 1. I like the idea of factoring and very effective.

The way I approach for number 1 was:-

9 (-27x-21) = 54 - 27Y

= -243x - 189 = 54 -27y
- 54 -54
____________________

-243x -243 = -27y
____ ___ ____ (divided by -27)
- 27 -27 -27

Y= 9x + 9

Why I am unable to obtain the same as you?? Is there something wrong I am going??
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by Rich@VeritasPrep » Fri Jun 04, 2010 4:07 pm
It looks like you actually did get the same thing as I did. We both got y=9x+9. In your original post, you had written y=9x-9, which is what I was correcting.

And yes, factoring is very effective. In this case, factoring saves a lot of time and makes calculations much easier. Multiplying 27*9 is not very time-effective, and remember, you're always looking for the quickest and simplest way to a solution.
Rich Zwelling
GMAT Instructor, Veritas Prep
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