Question

If y= a+b/ x where a, b are real number y= 1 and x=-1 and y =5 when x=-5 then a ,b =. (A)-1. (B)0. (C)11. (D)10

Answer 1

Question:-

If $\displaystyle\sf{y=a+\dfrac{b} {x} }$ for $\displaystyle\sf{a, \ b\in\mathbb{R} }$ such that $\displaystyle\sf{x=-1\implies y=1}$ and $\displaystyle\sf{x=-5\implies y=5}$ then find $\displaystyle\sf{a+b.}$

Answer:-

$\displaystyle\large\boxed{\sf{a+b=11} }$

Solution:-

Here,

$\displaystyle\longrightarrow\sf{y=a+\dfrac{b} {x} }$

For $\displaystyle\sf{x=-1,}$

$\displaystyle\longrightarrow\sf{y=1}$

$\displaystyle\longrightarrow\sf{a+\dfrac{b} {-1} =1}$

$\displaystyle\longrightarrow\sf{a-b=1\quad\quad\dots(1)}$

And for $\displaystyle\sf{x=-5,}$

$\displaystyle\longrightarrow\sf{y=5}$

$\displaystyle\longrightarrow\sf{a+\dfrac{b} {-5} =5}$

$\displaystyle\longrightarrow\sf{\dfrac{5a-b} {5} =5}$

$\displaystyle\longrightarrow\sf{5a-b=25}$

$\displaystyle\longrightarrow\sf{5(a-b) +4b=25}$

From (1),

$\displaystyle\longrightarrow\sf{5+4b=25}$

$\displaystyle\longrightarrow\sf{b=5}$

Then, again from (1),

$\displaystyle\longrightarrow\sf{a=6}$

Finally,

$\displaystyle\longrightarrow\sf{\underline{\underline{a+b=11}}}$