Question

Question:-
If x/a - y/b = 0 and ax + by = a²+b². Find the value of x and y by elimination method. ​

Answer 1

Answer:

Step-by-step explanation:

We have,

$\tt{\dfrac{x}{a}-\dfrac{y}{b}=0\,\,\,\,\,\,\,....(1)}\\\\\tt{a\,x\,\,+\,\,b\,y=\,a^2+b^2\,\,\,\,\,\,\,....(2)}$

From (1), we have,

$\tt{x=\dfrac{a}{b}y}$

Put this value in (2),

$\tt{a\,\cdot\dfrac{ay}{b}\,\,+\,\,b\,y=\,a^2+b^2}$

$\tt{\implies\,\dfrac{a^2y}{b}\,\,+\,\,b\,y=\,a^2+b^2}$

$\tt{\implies\,\dfrac{a^2y+b^2y}{b}=\,a^2+b^2}$

$\tt{\implies\,\dfrac{\left(a^2+b^2\right)y}{b}=\,a^2+b^2}$

$\tt{\implies\,\dfrac{y}{b}=1}$

$\tt{\implies\,y=b}$

So,

$\tt{x=a}$