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# Solving Simultaneous equations

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Senior Manager
Joined: 28 Mar 2012
Posts: 287
Concentration: Entrepreneurship
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
Followers: 23

Kudos [?]: 291 [1] , given: 23

Solving Simultaneous equations [#permalink]  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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Manager
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 [?]: 26 [0], given: 12

Re: Solving Simultaneous equations [#permalink]  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
Joined: 28 Mar 2012
Posts: 287
Concentration: Entrepreneurship
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
Followers: 23

Kudos [?]: 291 [0], given: 23

Re: Solving Simultaneous equations [#permalink]  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

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

Kudos [?]: 8 [0], given: 1

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

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!

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