Question

Find the value of x and y satisfying the following system:
ax + by = a, a(x + y) = a.
​​

Answer 1

Answer:

ax+by−a+b=0

x=

a

a−b−by

bx−ay−a−b=0

b(

a

a−b−by

)−ay=a+b

ab−b

2

−b

2

y−a

2

y=(a+b)a

−(a

2

+b

2

)y=a

2

+ab+b

2

−ab

y=

−(a

2

+b

2

)

a

2

+b

2

=−1

x=

a

a−b+b

=1

So x=1 & y=−1.