Question

For what value of k do the equations 3x - y + 8 = 0 and 6x - 4y = -16 represent coincident lines? ​

Answer 1

Correct Question :-

For what value of K for the equation 3x - y + 8 = 0 and 6x - ky = -16 represent coincident lines.

Understanding Concept :-

Linear equation is a equation which have highest power of degree is 1.and this equation can be represented as ax + bx + c = 0

For finding the types of line formed by quadratic equation are as follows :-

● a1x + b1x + c1 = 0

● a2x + b2x + c2 = 0

Now, Compare the values

if,

● a1 /a2 ≠ b1/b2 then it forms intersecting lines

● a1/a2 = b1/b2 = c1/c2 then it forms coincident lines

● a1/a2 = b1/b2 ≠ c1/c2 then it forms parallel lines

Solution :-

Here,

Two equations are given

● 3x - y + 8 = 0

● 6x - ky + 16 = 0

Compare the given equation with

a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0

Now, Condition for coincident lines

a1/a2 = b1/b2 = c1/c2

Here,

a1 = 3 , b1 = -1 , c1 = 8

and

a2 = 6 , b2 = -k , c2 = 16

Therefore,

3/6 = -1/-k = 8/16

1/2 = 1/k = 1/2

1/k = 1/2

k = 2

Hence, The value of K = 2 $.$

Answer 2

$\huge\ { \fbox{ \tt{ Answer}}}$

Linear equation is a equation which have highest power of degree is 1.and this equation can be represented as ax + bx + c = 0

For finding the types of line formed by quadratic equation are as follows :-

● a1x + b1x + c1 = 0

● a2x + b2x + c2 = 0

Now, Compare the values

if,

● a1 /a2 ≠ b1/b2 then it forms intersecting lines

● a1/a2 = b1/b2 = c1/c2 then it forms coincident lines

● a1/a2 = b1/b2 ≠ c1/c2 then it forms parallel lines

Solution :-

Here,

Two equations are given

● 3x - y + 8 = 0

● 6x - ky + 16 = 0

Compare the given equation with

a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0

Now, Condition for coincident lines

a1/a2 = b1/b2 = c1/c2

Here,

a1 = 3 , b1 = -1 , c1 = 8

and

a2 = 6 , b2 = -k , c2 = 16

Therefore,

3/6 = -1/-k = 8/16

1/2 = 1/k = 1/2

1/k = 1/2

k = 2

Hence, The value of K = 2 ..

Answer sahi hai values alag hai....XD

hope it helps ✨