Question

if the lines given by 2x+ky=1 and 3x-5y=7 are parallel then the value of k​

Answer 1

Answer:

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Answer 2

Answer:-

Given:-

Two lines 2x + ky = 1 and 3x - 5y = 7 are parallel.

We know that,

Two lines are parallel if they have equal slopes.

So , we can find the slope of each line given through the slope - intercept form.

i.e., y = mx + c

Let the slope of 2x + ky = 1 be m₁.

⟹ 2x + ky = 1

⟹ ky = 1 - 2x

⟹ y = (1 - 2x)/k

⟹ y = (- 2/k)x + 1/k

It is in the form of y = mx + c. So,

• m₁ = - 2/k

Now,

Let the slope of 3x - 5y = 7 be m₂.

Similarly,

⟹ 3x - 5y = 7

⟹ 3x - 7 = 5y

⟹ (3x - 7)/5 = y

⟹ (3/5)x - 7/5 = y

Therefore,

• m₂ = 3/5.

Now,

We know,

Slope of first line (m₁) = Slope of second line (m₂).

⟹ - 2/k = 3/5

⟹ - 2 × 5 = 3k

⟹ - 10/3 = k

∴ Required value of k is - 10/3.