Question

if a pair of linear equationd 3x+2ky=2 and 2x+5y+1=0 are parallel to each other then the value of 'k'​

Answer 1

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

Step-by-step explanation:

There are three methods for this pair of linear equations to be solved.

1. Substitution Method

2. Elimination Method.

3. Cross Multiplication method

Here we will use the substitution method.

1. 3x+2ky=2

2x+5y+1=0

hi

=> 2x+5y+1=0

=> 2x+5y=-1

=> 2x=-1-5y

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

Substituting values of X in equation 1.

=> 3x+2ky=2

=> 3{(-1-5y)/2} + 2ky = 2