Question

Solve for x and y:

217x + 131y = 913, 131x + 217y = 827

Answer 1

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

⇒ y = 2

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