Question

for which value of 'k' the following pairs of linear equations are parallel 2x+3y=5 and 4x+k y =8​

Answer 1

Answer:  The value of $k$ is  $6$ for which the linear equations $2x+ 3y=\,5$ and  $4x+ky=\, 8$ are parallel.

Step-by-step explanation: The given linear equations are of straight lines.

Two straight lines are parallel if their slopes are equal.

For a equation $y=\, mx+c$, its slope is $m$ and $x$- intercept is $c$.

Now, we need to convert the given equations in the general form mentioned above.

so, $\begin{align}2x+ 3y &= 5\\y &= \frac{5}{3}- \frac{2x}{3}\end{align}$$2x+ 3y=\,5$

$\begin{equation}\implies y =\,- \frac{2x}{3}+ \frac{5}{3}. \qquad \end{equation}$

and, $4x+ky=\, 8$

$\begin{equation*} \tag{2} \implies y= \, - \frac{4x}{k} +\frac{8}{k} \qquad \end{equation*}$ .         $(2)$      

From equations $(1) \,\text{and}\,(2)$ , we get slopes $\frac{-2}{3}\,\text{and}\, \frac{-4}{k}$ respectively.

Since lines are parallel, therefore $\frac{-2}{3}=\,\frac{-4}{k}$

which gives $k=\,6$.