Question

18. If the lines given by 3x + 2ky =2 and 2x + 5y = 1 are parallel, then the value of k is *
(a) (-5)/4
(b) 2/5
(c) 15/4
(d) 3/2

Answer 1

Answer:

If the lines given by 3x + 2ky = 2 and 2x + 5y + 1 = 0 are parallel, then what is the value of k?

For the lines to be parallel, the slopes of the lines MUST be equal.

Lines:

3x + 2ky - 2 = 0 … (1)

2x + 5y + 1 = 0 … (2)

Now, convert 1 and 2 into y = mx + c form where m is the slope.

for 1,

y = (-3/2k)x + (1/k)

for 2,

y = (-2/5)x - (1/5)

So now for both lines to be parallel, (-3/2k) must be equal to (-2/5)

Solving for k, we get {k = 15/4}

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Answer 2

Answer :

k = 15/4 (option c)

Note:

★ A linear equation is two variables represent a straight line .

★ The word consistent is used for the system of equations which consists any solution .

★ The word inconsistent is used for the system of equations which doesn't consists any solution .

★ Solution of a system of equations : It refers to the possibile values of the variable which satisfy all the equations in the given system .

★ A pair of linear equations are said to be consistent if their graph ( Straight line ) either intersect or coincide each other .

★ A pair of linear equations are said to be inconsistent if their graph ( Straight line ) are parallel .

★ If we consider equations of two straight line

ax + by + c = 0 and a'x + b'y + c' = 0 , then ;

• The lines are intersecting if a/a' ≠ b/b' .

→ In this case , unique solution is found .

• The lines are coincident if a/a' = b/b' = c/c' .

→ In this case , infinitely many solutions are found .

• The lines are parallel if a/a' = b/b' ≠ c/c' .

→ In this case , no solution is found .

Solution :

Here ,

The given linear equations are ;

3x + 2ky = 2

2x + 5y = 1

The given equations can be rewritten as ;

3x + 2ky - 2 = 0

2x + 5y - 1 = 0

Clearly , we have ;

a = 3

a' = 2

b = 2k

b' = 5

c = -2

c' = -1

Now ,

a/a' = 3/2

b/b' = 2k/5

c/c' = -2/-1 = 2

For the given equations to be parallel ,

a/a' = b/b' ≠ c/c'

Here ,

It is clear that , a/a’ ( = 3/2 ) ≠ c/c' ( = 2 )

Hence ,

The lines will be parallel if a/a' = b/b'

=> 3/2 = 2k/5

=> (3/2)×(5/2) = k

=> k = 15/4

Hence ,

k = 15/4 (option c)