Question

$\frak{\pmb{\underline{Question}}}:-$

1) If the lines given by 4x + (k+1)y = 2 and 5x + (k+2)y = 1 are parallel, then the value of k is _____

(a) 1

(b) 2

(c) 3

(d) 4​

Answer 1

Answer:

• Option (C) 3 is correct

Step-by-step explanation:

We are given that the given equation of lines are parallel to each other. Parallel lines have same slope. Therefore both the given equations must have same slope.

In general, for any line whose equation is ax + by + c = 0, it's slope is given by:

• m = - Coefficient of x/coefficient of y

Here m is the slope of the line.

For the first equation, slope is given by:

=> - coefficient of x/coefficient of y

=> - 4/(k + 1) ...Eq(1)

For the second equation, slope is given by:

=> - Coefficient of x/coefficient of y

=> - 5/(k + 2) ...Eq(2)

Since we already discussed that the base condition for lines to be parallel to each other, their slopes must be same.

Therefore eq(1) must be equal to eq(2)

=> -4/(k + 1) = -5/(k + 2)

=> 4/(k + 1) = 5/(k + 2)

=> 4(k + 2) = 5(k + 1)

=> 4k + 8 = 5k + 5

=> 8 - 5 = 5k - 4k

=> 3 = k

So the required value of k is 3.

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Answer 2

Answer

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