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# simultaneous and linear equations

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Intern
Joined: 21 Sep 2013
Posts: 27
Location: United States
Concentration: Finance, General Management
GMAT Date: 10-25-2013
GPA: 3
WE: Operations (Mutual Funds and Brokerage)
simultaneous and linear equations  [#permalink]

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28 Oct 2013, 01:23
2
Finding values of X and Y in linear simultaneous equations can be very easy. just follow the method mentioned below.

firstly our formula to find X=numerator/denominator and Y=numerator/denominator.
ideally if we have value for any one variable we need not calculate the value for the other variable , as it can be easily substituted in the equation.

say our 2 equations are
2x+4y=10
3x+2y=11

As per our formula x= Num/deno.
now numerator is obtained by cross multiplying (4*11) and subtracting from it the cross product of (2*10)=44-20=24
and denominator is obtained by cross multiplying (4*3) and subtracting from it the cross product of (2*2)=12-4=8

therefore our value for x = Num/Den = 24/8=3

now we can find the value of Y in similar way. however, it will be time consuming . thus we just substitute the value of X in one of the variable.
2x+4y=10
2(3)+4y=10
y=1

therefore we get our two variables x=3,y=1.

hope this helps for quicker calculations.

For those who are curious how to find value of Y in a similar way the method is mentioned below.
i ll just retype the previous equations for better understanding

2x+4y=10
3x+2y=11

again for Y the same formula=Num/ Den ( but the multiplication is slightly different)
now numerator is obtained by cross multiplying (2*11) and subtracting from it the cross product of (3*10)=22-30=-8
and denominator is obtained by cross multiplying (2*2) and subtracting from it the cross product of (4*3)=4-12=-8

thus Y=num/den=-8/-8=1
y=1.

now we can find the value of X, by substituting the value of Y in any equations, as we did above.
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Joined: 09 Sep 2013
Posts: 12515
Re: simultaneous and linear equations  [#permalink]

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19 Sep 2018, 12:27
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Re: simultaneous and linear equations   [#permalink] 19 Sep 2018, 12:27
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# simultaneous and linear equations

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