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