Question

if the lines 3x+2ky-2=0 and 2x+5y+1=0 are parallel, then what is the value of k?
3/4
15/4
4/5
8/9

Answer 1

Answer:

Hello

Step-by-step explanation:

15/4 is the correct answer.

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}

Answer 2

Solution :-

Given two linear equations are ,

• 3x + 2ky - 2 = 0.
• 2x + 5y + 1 = 0 .

Since the lines are parallel , then the lines will have no solution . Since the line will not intersect each other , then we know the Condition of two lines to be parallel

• a1 x + b1 y + c1 = 0.
• a2 x + b2 y + c2 = 0 .

★The Condition is :-

$\boxed{\red{\bf \dagger \dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq\dfrac{c_1}{c_2}}}$

So here ,

➳ a 1/ a2 = b 1/ b 2

➳ 3/2 = 2k/5.

➳ k = 3/2 × 5/2

➳ k = 15/4.

Hence the value of k is 15/4 .