Given,

ax + by = a + b    .................1

2ax + 2by = 2     ..................2

Multiply by 2 in equation 1, we get

2ax + 2by = 2(a + b)   ..........3

From equation 2 and 3, we find that for ax + by, we get two answer i.e. 2 and 2(a + b) which is not possible.

So, this sytem of equation has no solution.