Question

if the system of equations6x+2y=3and kx+y=2 has a unique solution,find the value of k​

Answer 1

Answer:

except 3

Step-by-step explanation:

Two lines

ax+by=c………(1)

and

cx+dy=e……..(2)

Are has a unique solution

If

a/c ≠ b/d.

In the given equation

a=k , b=(-1), c=6, d=(-2).

So by the condition

k/6 ≠ (-1/-2)

Or, k/6 ≠ 1/2

Or, k ≠ 3.

So for any real value k except 3.

Answer 2

Step-by-step explanation:

6x + 2y = 3

for x

6x + 2y = 3

6x =3 - 2y

6x/6 = 3 - 2y /6

x = 3 - 2y / 6

x = -y/ 3 + 1 / 2

for y

6x + 2y = 3

2y= 3-6x

2y/2 = 3 - 6x / 2

y = 3 - 6x / 2

y = 3 / 2 - 3x

kx + y = 2

for k

ky + y =2

ky = 2 - y

yk / y = 2 - y / y

k = 2 - y / y

k = -1 + 2 / y

for y

ky + y = 2

( k + 1 ) y = 2

( k + 1 ) y / k +1 = 2 / k + 1

y = 2 / k + 1

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