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Solving Simultaneous equations

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Senior Manager
Senior Manager
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Joined: 29 Mar 2012
Posts: 287
Concentration: Entrepreneurship
Schools: Kellogg, Kellogg '19
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
Followers: 25

Kudos [?]: 322 [1] , given: 23

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Solving Simultaneous equations [#permalink]

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New post 04 Jun 2012, 07:39
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Hi,

Consider following equations:
\(a_1x+b_1y=c_1\)
\(a_2x+b_2y=c_2\)

To get the value of x & y
\(x=(c_1b_2-c_2b_1)/(a_1b_2-a_2b_1)\)
\(y=(a_1c_2-a_2c_1)/(a_1b_2-a_2b_1)\)
This is Cramer's rule
Remember to reduce the equations in the above mentioned form.

For example:
2x+3y=1
7x+6y=8

According to the Cramer's rule,
\(x=(1*6-8*3)/(2*6-7*3)=2\)
\(y=(2*8-7*1)/(2*6-7*3)=-1\)


Regards,
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Manager
Manager
avatar
Joined: 03 Feb 2012
Posts: 56
Location: United States (WI)
Concentration: Other
Schools: University of Wisconsin (Madison) - Class of 2014
GMAT 1: 680 Q46 V38
GMAT 2: 760 Q48 V46
GPA: 3.66
WE: Marketing (Manufacturing)
Followers: 0

Kudos [?]: 27 [0], given: 12

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Re: Solving Simultaneous equations [#permalink]

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New post 04 Jun 2012, 18:31
Seems like a lot of work. Would it not be quicker in your example to solve as follows:

\(2x+3y=1\)
\(7x+6y=8\)

Multiply top equation by two:

\(4x+6y=2\)
and
\(6y=2-4x\)

Substitute in second equation, solve for x

\(7x+2-4x=8\)
\(3x=6\)
\(x=2\)

Solve for y in either

\(2*2+3y=1\)
\(4+3y=1\)
\(3y=-3\)
\(y=-1\)
Senior Manager
Senior Manager
User avatar
Joined: 29 Mar 2012
Posts: 287
Concentration: Entrepreneurship
Schools: Kellogg, Kellogg '19
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
Followers: 25

Kudos [?]: 322 [0], given: 23

GMAT ToolKit User
Re: Solving Simultaneous equations [#permalink]

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New post 05 Jun 2012, 01:04
Hi,

It is useful in long run. One has to practice to get used to this forumla, then it could be used conviniently.

Regards,

nsspaz151 wrote:
Seems like a lot of work. Would it not be quicker in your example to solve as follows:

\(2x+3y=1\)
\(7x+6y=8\)

Multiply top equation by two:

\(4x+6y=2\)
and
\(6y=2-4x\)

Substitute in second equation, solve for x

\(7x+2-4x=8\)
\(3x=6\)
\(x=2\)

Solve for y in either

\(2*2+3y=1\)
\(4+3y=1\)
\(3y=-3\)
\(y=-1\)
Intern
Intern
User avatar
Joined: 23 Apr 2012
Posts: 2
Location: Jamaica
Concentration: Marketing, Statistics
GMAT Date: 09-26-2012
WE: Psychology and Counseling (Education)
Followers: 0

Kudos [?]: 9 [0], given: 1

Re: Solving Simultaneous equations [#permalink]

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New post 14 Jun 2012, 08:06
Hey cyberjadugar,

This is really handy! Thanks for sharing this. It seems familiar, but I've been out of school for so long, I would swear that most of things I am re-learning I was never taught! I'm going to check if it works with fractions. Kudos man!

Cheers,

toni
_________________

Moving ahead requires discipline, drive and dogged self belief that you can do it!

Intern
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Joined: 28 Apr 2016
Posts: 2
Followers: 0

Kudos [?]: 0 [0], given: 1

Re: Solving Simultaneous equations [#permalink]

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New post 20 May 2016, 22:40
cyberjadugar wrote:
Hi,

It is useful in long run. One has to practice to get used to this forumla, then it could be used conviniently.

Regards,

nsspaz151 wrote:
Seems like a lot of work. Would it not be quicker in your example to solve as follows:

\(2x+3y=1\)
\(7x+6y=8\)

Multiply top equation by two:

\(4x+6y=2\)
and
\(6y=2-4x\)

Substitute in second equation, solve for x

\(7x+2-4x=8\)
\(3x=6\)
\(x=2\)

Solve for y in either

\(2*2+3y=1\)
\(4+3y=1\)
\(3y=-3\)
\(y=-1\)


Will we consider the signs of the coefficients while multiplying ?
Re: Solving Simultaneous equations   [#permalink] 20 May 2016, 22:40
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Solving Simultaneous equations

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