Question

5. Solve 4x -3y + 17 = 0 and 5x + y + 7 = 0 and hence find the value of n for which y = nx -1

Based on elimination method.​

Answer 1

Answer:

$\sf{The \ value \ of \ n \ is \ -2.}$

Given:

$\sf{The \ given \ equations \ are:}$

$\sf{\leadsto{4x-3y+17=0}}$

$\sf{\leadsto{5x+y+7=0}}$

$\sf{\leadsto{y=nx-1}}$

To find:

$\sf{The \ value \ of \ n.}$

Solution:

$\sf{The \ given \ equations \ are:}$

$\sf{\leadsto{4x-3y+17=0}}$

$\sf{\therefore{4x-3y=-17...(1)}}$

$\sf{\leadsto{5x+y+7=0}}$

$\sf{\therefore{5x+y=-7...(2)}}$

$\sf{\leadsto{y=nx-1...(3)}}$

$\sf{Multiply \ equation (2) \ by \ 3, \ we \ get}$

$\sf{15x+3y=-21...(4)}$

$\sf{Add \ equations \ (1) \ and \ (4), \ we \ get}$

$\sf{4x-3y=-17}$

$\sf{+}$

$\sf{15x+3y=-21}$

__________________

$\sf{19x=-38}$

$\sf{\therefore{x=\dfrac{-38}{19}}}$

$\boxed{\sf{\therefore{x=-2}}}$

$\sf{Substitute \ x=-2 \ in \ equation (2), \ we \ get}$

$\sf{5(-2)+y=-7}$

$\sf{\therefore{-10+y=-7}}$

$\sf{\therefore{y=-7+10}}$

$\boxed{\sf{\therefore{y=3}}}$

$\sf{Substitute \ x=-2 \ and \ y=3 \ in \ equation (3)}$

$\sf{3=n(-2)-1}$

$\sf{\therefore{3=-2n-1}}$

$\sf{\therefore{2n=-4}}$

$\sf{\therefore{n=\dfrac{-4}{2}}}$

$\boxed{\sf{\therefore{n=-2}}}$

$\sf\purple{\tt{\therefore{The \ value \ of \ n \ is \ -2.}}}$