Solve for x and y: 217x + 131y = 913, 131x + 217y = 827

1.	Solve for x and y: 217x + 131y = 913, 131x + 217y = 827
Answer» The given equations are: 217x + 131y = 913 …..(i) 131x + 217y = 827 ……(ii) On adding (i) and (ii), we get: 348x + 348y = 1740 ⇒348(x + y) = 1740 ⇒x + y = 5 ……(iii) On subtracting (ii) from (i), we get: 86x – 86y = 86 ⇒86(x – y) = 86 ⇒x – y = 1 ……(iv) On adding (iii) from (i), we get: 2x = 6 ⇒x = 3 On substituting x = 3 in (iii), we get: 3 + y = 5 ⇒y = 5 – 3 = 2 Hence, the required solution is x = 3 and y = 2.

Answer»

The given equations are:

217x + 131y = 913 …..(i)

131x + 217y = 827 ……(ii)

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

348x + 348y = 1740

⇒348(x + y) = 1740

⇒x + y = 5 ……(iii)

On subtracting (ii) from (i), we get:

86x – 86y = 86

⇒86(x – y) = 86

⇒x – y = 1 ……(iv)

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

2x = 6

⇒x = 3

On substituting x = 3 in (iii), we get:

3 + y = 5

⇒y = 5 – 3 = 2

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

Discussion