53x+47y=271 47x+53y=229 solve the following system of equation
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\textbf{Answer :}Answer :
The given equations are
53x + 47y = 271 ...(i)
47x + 53y = 229 ...(ii)
Now, multiplying (i) by 47 and (ii) by 53, we get
2491x + 2209y = 12737
2491x + 2809y = 12137
On subtraction, we get
600y = - 600
or, y = - 1
Now, putting y = - 1 in (i), we get
53x + 47 (- 1) = 271
or, 53x = 271 + 47
or, 53x = 318
or, x = 318/53
or, x = 6
Therefore, the required solution be
\bold{x = 6}x=6 and \bold{y = - 1}y=−1
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