if 49x+51y=499 ,51x+49y=501, find the value of x and y

 if 49x+51y=499 ,51x+49y=501, find the value of x and y

 

Here note the coefficients of x and y are interchanged in the two equations

so we add and subtract the two equations and get two new equations which we will solve

 

49x + 51y = 499

51x +49y = 501

_________________add

100x+100y=1000     divide by 100

x+y=10---------------{1} 

49x + 51y = 499

51x +49y = 501

_________________subtract

-2x+2y=-2          divide by (-2) 

x-y =1 ------------{2}

now we try to solve the new equations {1} and {2}

x+y=10---------------{1}

x-y =1 ------------{2}

--------------------------------add

2x =11

x=(11/2)

substitute in x+y=10

(11/2)+y=10

y=10-(11/2)=(9/2)

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