Question

Find the value of k, so that the pair of equations 2x+5y-7=0 and kx-10y+14=0 represent coincident lines.​

Answer 1

Answer:

-4

2/x=5/-10=-7/14

2/x=-1/2

x=-4

Answer 2

Given:

the pair of equations 2x+5y-7=0 and kx-10y+14=0 represent coincident lines.​

To Find:

Find the value of k

Solution:

Two lines are said to be coincident if they lie on top of each other, from this statement we can that the slope of both the lines will be the same, to find the value of k first we will be express the equation in the form,

y=mx+c

where m is the slope of the line and c is the constant

Now

$2x+5y-7=0\\y=\frac{-2}{5}x+\frac{7}{5}$

And

$kx-10y+14=0\\y=\frac{k}{10}x +\frac{7}{5}$

Now to find the value of k we need to equate both the slopes, which goes as,

$\frac{-2}{5} =\frac{k}{10} \\k=-4$

Hence, the value of k is -4.