Question

Prove that the values of x obtained from the equations ax²+by²=1 and ax+by=1 will be equal if a+b=1.

Answer 1

Given a+b=1=>b=1-a

From equation (1)
ax^2+by^2=1

=>x^2 = (1-(1-a)y^2)/a
= ((a-1)y^2+1)/a

From equation (1)

ax+by=1

=>x =(1-(1-a)y)/a
=((a-1)y+1)/a

=>x^2 =((a-1)^2y^2+1-2(a-1)y))/a^2




simplyfying this you get the answer of x^2 in equation 1