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Solving Simultaneous equations

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Senior Manager
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Solving Simultaneous equations [#permalink] New post 04 Jun 2012, 06:39
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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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My posts: Solving Inequalities, Solving Simultaneous equations, Divisibility Rules

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Joined: 03 Feb 2012
Posts: 56
Location: United States (WI)
Concentration: Other
Schools: University of Wisconsin (Madison) - Class of 2014
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GMAT 2: 760 Q48 V46
GPA: 3.66
WE: Marketing (Manufacturing)
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Kudos [?]: 24 [0], given: 12

Re: Solving Simultaneous equations [#permalink] New post 04 Jun 2012, 17:31
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: 28 Mar 2012
Posts: 285
Concentration: Entrepreneurship
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
Followers: 16

Kudos [?]: 157 [0], given: 23

GMAT ToolKit User GMAT Tests User
Re: Solving Simultaneous equations [#permalink] New post 05 Jun 2012, 00:04
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

_________________

My posts: Solving Inequalities, Solving Simultaneous equations, Divisibility Rules

My story: 640 What a blunder!

Vocabulary resource: EdPrep

Facebook page: fb.com/EdPrep

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Re: Solving Simultaneous equations [#permalink] New post 14 Jun 2012, 07:06
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
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Re: Solving Simultaneous equations   [#permalink] 14 Jun 2012, 07:06
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