Question

On solving $19x+17y=55,17x+19y=53,$ we get:
(a) x = 3, y = 2
(b) x = 3, y = −2
(c) x = 2, y = 1
(d) x = 5, y = −3

Answer 1

The correct option is (c).
19x + 17y = 55 ....(i)
17x + 19y = 53 ....(ii)
On adding (i) and (ii), we get:
36x + 36y = 108
36(x + y) = 108
(x + y) = 3 ....(iii)
On subtracting (ii) from (i), we get:
2x − 2y = 2
2(x − y) = 2
⇒ (x − y) = 1 ....(iv)
Again, on adding (iii) and (iv), we get:
2x = 4 ⇒ x = 2
On substituting x = 2 in (iii), we get:
y = 1
∴​ x = 2 and y = 1