Question

$ax + by = a + b \\ ax + b(x + y) = a + b$
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Answer 1

Let us consider,
ax+by=a+b---(1)
ax+b(x+y)=a+b----(2)
Equate(1) & (2)..,,
ax+by=ax+b(x+y)
by=b(x+y)
y=b(x+y) / b
y=x+y
x=y-y
x=0
substitute x=0 in (1)..,
ax+by=a+b
a(0)+by=a+b
by=a+b
y=a+b/b

Answer 2

ax+by=a+b....(i)
ax+b(x+y)=a+b.....(ii)
In (i),
$ax = a + b - by \\ substituting \: value \: in \: ii \\ a + b - by + bx + by = a + b \\ = > bx = 0 \\ = > x = 0$
$y = \frac{a+b}{b}$