Question

3. If the pair of equations 8x + 2y = 5k and 4x + y = 3 represent coincident lines, then

(a) k=- 5/6
(b) k= 6/5
(c) k= 5/6
(d) k = -6/5​

Answer 1

$\textbf{Given:}$

$\textsf{8x+2y=5k}$

$\mathsf{4x+y=3\;represent\;coincident\;lines}$

$\textbf{To find:}$

$\textsf{The value of k}$

$\textbf{Solution:}$

$\textsf{Since the lines are coincident, their corresponding coefficients }$

$\textsf{are proportional in their equations}$

$\mathsf{\dfrac{8}{4}=\dfrac{2}{1}=\dfrac{5k}{3}}$

$\implies\mathsf{2=2=\dfrac{5k}{3}}$

$\implies\mathsf{5k=6}$

$\implies\boxed{\mathsf{k=\dfrac{6}{5}}}$

$\textbf{Answer:}$

$\mathsf{Option\;(b)\;is\;correct}$

$\textbf{Find more:}$

Find the value of P and Q for which the following system of equations has infinitely many solutions:(2p- 1)x + 3y= 5 and 3x+ (q- 1)y=2​

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