An important and exam oriented question from linear equations in two variables in which we have given two equations 71x+37y=253, 37x+71y=287 and we have to find the value of variables x and y from the given equations

Kindly solve the equations in a detailed manner

RS Aggarwal, Class 10, chapter 3B, question no 32

The given equations are:

71x + 37y = 253 …..(i)

37x + 71y = 287 ……(ii)

On adding (i) and (ii), we get:

108x + 108y = 540

⇒108(x + y) = 540

⇒(x + y) = 5 ……(iii)

On subtracting (ii) from (i), we get: 34x – 34y = -34

⇒34(x – y) = -34

⇒(x – y) = -1 ……(iv)

On adding (iii) from (i), we get:

2x = 5 – 1 = 4

⇒x = 2

On subtracting (iv) from (iii), we get:

2y = 5 + 1 = 6

⇒y = 3

Hence, the required solution is x = 2 and y = 3