Question:
solve by cross multiplication method- x y = a b , ax - by = a square - b square
Answer:
Given,
x + y = a + b ....................1
ax - by = a2 - b2 .....................2
Multiply by b in equation 1 we, get
bx + by = ab + b2 ....................3
Add equation 2 and 3, we get
ax - by + bx + by = (a2 - b2 ) + (ab + b2 )
=> ax + bx = a2 - b2 + ab + b2
=> x(a + b) = a2 + ab
=> x(a + b) = a(a + b)
=> x = a(a + b)/(a + b)
=> x = a
From equation 3, put the value of x, we get
ab + by = ab + b2
=> by = ab + b2 - ab
=> by = b2
=> y = b2 /b
=> y = b
So, x = a and y = b
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