Question

4x +6/y=15 , 6x-8/y=14:y is not equal to 0
Find p if y = px -2

Answer 1

$\huge\purple{\underline{\underline{\pink{Ans}\red{wer:}}}}$

$\sf{The \ value \ of \ p \ is \ \frac{1232}{969}}$

$\sf\orange{Given:}$

$\sf{\implies{4x+\frac{6}{y}=15}}$

$\sf{\implies{6x-\frac{8}{y}=14}}$

$\sf{=>y \ is \ not \ equal \ to \ zero.}$

$\sf\pink{To \ find:}$

$\sf{The \ value \ p.}$

$\sf\green{\underline{\underline{Solution:}}}$

$\sf{\implies{4x+\frac{6}{y}=15...(1)}}$

$\sf{\implies{6x-\frac{8}{y}=14...(2)}}$

$\sf{Multiply \ equation (1) \ by \ 3, \ we \ get}$

$\sf{\implies{12x+\frac{18}{y}=45...(3)}}$

$\sf{Multiply \ equation (2) \ by \ 2, \ we \ get}$

$\sf{\implies{12x-\frac{16}{y}=28...(4)}}$

$\sf{Subract \ equation (4) \ from \ equation (3)}$

$\sf{12x+\frac{6}{y}=45}$

$\sf{-}$

$\sf{12x-\frac{16}{y}=28}$

__________________________________

$\sf{\frac{6}{y}+\frac{16}{y}=17}$

$\sf{\frac{22}{y}=17}$

$\sf{22=17y}$

$\sf{\therefore{y=\frac{22}{17}}}$

$\sf{Substituting \ y=\frac{22}{17} \ in \ equation (1)}$

$\sf{4x+\frac{6}{\frac{22}{17}}=15}$

$\sf{\therefore{4x+\frac{6×17}{22}=15}}$

$\sf{4x+\frac{3×17}{11}=15}$

$\sf{4x+\frac{51}{11}=15}$

$\sf{4x=15-\frac{51}{11}}$

$\sf{4x=\frac{165}{11}-\frac{51}{11}}$

$\sf{4x=\frac{165-51}{11}}$

$\sf{4x=\frac{114}{11}}$

$\sf{x=\frac{57}{22}}$

$\sf{\therefore{Value \ of \ x \ is \ \frac{57}{22} \ and \ y \ is \frac{22}{17}}}$

_________________________________

$\sf{\implies{y=px-2}}$

$\sf{\frac{22}{17}=p×\frac{57}{22}-2}$

$\sf{\therefore{p×\frac{57}{22}=\frac{22}{17}+2}}$

$\sf{p×\frac{57}{22}=\frac{22+34}{17}}$

$\sf{p×\frac{57}{22}=\frac{56}{17}}$

$\sf{\therefore{p=\frac{56×22}{17×57}}}$

$\sf{\therefore{p=\frac{1232}{969}}}$

$\sf\purple{\tt{\therefore{The \ value \ of \ p \ is \ \frac{1232}{969}}}}$