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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
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.
simultaneous and linear equations
28 Oct 2013, 01:23