Question

The value of k for which the lines represented by the following pair of linear equations are coincident is 2x + 3y + 7 = 0 8x + 12y + k = 0

Answer 1

Step-by-step explanation:

Given :-

The pair of linear equations are 2x + 3y + 7 = 0 8x + 12y + k = 0

To find :-

Find the value of k for which the lines represented by the following pair of linear equations are coincident ?

Solution :-

Given that

The pair of linear equations are

2x + 3y + 7 = 0

On comparing with a1x+b1y+c1 = 0

a1 = 2

b1 = 3

c1 = 7

and

8x + 12y + k = 0

On comparing with a2x+b2y+c2 = 0

a2 = 8

b2 = 12

c2 = k

We know that

If the pair of linear equations in two variables a1x+b1y+c1 = 0 and a2x+b2y+c2 = 0 are coincident lines then

a1/a2 = b1/b2 = c1/c2

Given that

Given lines are coincident

=> a1/a2 = b1/b2 = c1/c2

=> 2/8 = 3/12 = 7/k

=> 1/4 = 1/4 = 7/k

=> 1/4 = 7/k

On applying cross multiplication then

=> k×1 = 7×4

=> k = 28

Therefore, k = 28

Answer:-

The value of k for the given problem is 28

Used formulae:-

→ If the pair of linear equations in two variables a1x+b1y+c1 = 0 and a2x+b2y+c2 = 0 are coincident lines then a1/a2 = b1/b2 = c1/c2

Points to know:-

If the pair of linear equations in two variables a1x+b1y+c1 = 0 and a2x+b2y+c2 = 0 then

→ They are coincident lines then

a1/a2 = b1/b2= c1/c2

→ They are parallel lines then

a1/a2 = b1/b2 ≠ c1/c2

→ They are intersecting lines then

a1/a2 ≠ b1/b2 ≠ c1/c2

Answer 2

Answer:

k = 28.

Step-by-step explanation:

If the lines are coincident then their equations will be differ in a scalar quantity I.e, second line equation will be the times of first line equation.

So, z × (2x + 3y + 7) = 8x + 12y + k

then 2z = 8; 3z = 12; and 7z = k

$z = \frac{8}{2} = \frac{12}{3} = \frac{k}{7 } \\ from \: the \: above \: equation \: z = 4 \\ then \: 4 = \frac{k}{7} \\ so \: k = 7 \times 4 = 28$