Question

find those integral values of m for which the X co-ordinate of the point of intersection of the lines represented by Y is equal to MX + 1 and 3 X + 4 Y is equal to 9 is an integer

Answer 1

$\textbf{Given:}$

$\textsf{Lines are}$

$\mathsf{y=mx+1\;and\;3x+4y=9}$

$\textbf{To find:}$

$\textsf{Integral values of m for which the x co-ordinate}$

$\textsf{of point of intersection is an integer}$

$\textbf{Solution:}$

$\textsf{By solving the given equations,we can find out point of intersection of the given lines}$

$\mathsf{y=mx+1}$--------(1)

$\mathsf{3x+4y=9}$---------(2)

$\mathsf{Using (1) in (2)}$

$\mathsf{3x+4(mx+1)=9}$

$\mathsf{3x+4mx+4=9}$

$\mathsf{3x+4mx=5}$

$\mathsf{(3+4m)x=5}$

$\implies\mathsf{x=\dfrac{5}{4m+3}}$

$\mathsf{From\;(1)}$

$\mathsf{y=\dfrac{5m}{4m+3}+1}$

$\mathsf{y=\dfrac{5m+4m+3}{4m+3}}$

$\mathsf{y=\dfrac{9m+3}{4m+3}}$

$\therefore\mathsf{The\;point\;of\;intersection\;is\;\left(\dfrac{5}{4m+3},\dfrac{9m+3}{4m+3}\right)}$

$\textsf{But x co-ordinate is an integer}$

$\implies\mathsf{\dfrac{5}{4m+3}\;is\;an\;integer}$

$\implies\mathsf{4m+3=\pm5,\;\pm1}$

$\mathsf{4m+3=5\;\implies\;m=\dfrac{1}{2}\;is\;not\;an\;integer}$

$\mathsf{4m+3=-5\;\implies\;m=-2\;is\\;an\;integer}$

$\mathsf{4m+3=1\;\implies\;m=\dfrac{-1}{2}\;is\;not\;an\;integer}$

$\mathsf{4m+3=-1\;\implies\;m=-1\;is\;an\;integer}$

$\therefore\underline{\textbf{The possible values of m are -2 and -1}}$

Answer 2

Question :- find those integral values of m for which the X co-ordinate of the point of intersection of the lines represented by Y is equal to MX + 1 and 3 X + 4 Y is equal to 9 is an integer

Correct Answer in the Attachment

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©A. Pal_yt