Question

4.If the lines given by 6x + 4ky =
44 2x + 5y + 1 = 0 are parallel,
then the value of k is
20/3

15/4

15/3
17/4

Answer 1

Answer:

We are given with two simultaneous pair of equations which when made in graphs are parallel to each other.

GiveN equations:

• 6x + 4ky - 44 = 0
• 2x + 5y + 1 = 0

We need to find the value of k for which the above lines are parallel to each other.

Condition for parallel lines:

If there are two pair of linear equations in two variable:

• $\rm{a_1x + b_1y + c_1 = 0}$
• $\rm{a_2x + b_2y + c_2 = 0}$

Then a1 / a2 = b1 / b2 ≠ c1 / c2 which are coefficients and constant term of the equations.

━━━━━━━━━━━

We have to compare the given equations with the above equations in a1, b1.... to plug in required relation.

By applying the above condition:

$\rm{ \dfrac{6}{2} = \dfrac{4k}{5} \not = \dfrac{ - 44}{1} \: }$

Now cross multiplying,

$\rm{4k = 15 }$

Dividing 4 from both sides,

$\rm{k = \dfrac{15}{4} }$

Now as we have got our required answer, let's check with not equals to condition too...

$\rm{ \dfrac{4( \dfrac{15}{4} )}{5} = 3 \: which \: is \not = \dfrac{ - 44}{1} }$

So, required value for k for which the above lines are parallel is:

$\large{ \boxed{ \sf{ \red{k = \dfrac{15}{4}}}} }$

And we are done !!