Question

Find the value(s) of 'k' for which the pair of equations kx+2y=3 and 3x+6y=10 has a unique solution.

Answer 1

kx+2y=3

now,

y=3-kx/2 eq1

3x+6y=10

y=10-3x/6 eq2

now put these eqs equal.

3-kx/2 = 10-3x/6

now cross multiplication.

6(3-kx) = 2(10-3x)

18 - 6kx = 20 - 6x

18 - 6k = 20 - 6

18 - 6k = 14

18 - 14 = 6k

4/6 = k

2/3 = k

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Answer 2

Answer:

Value of k is all integers other than 1.

Step-by-step explanation:

Given Pair of equations,

kx + 2y = 3

3x + 6y = 10

Pair of equations has unique solution.

To find: Value of k.

We know that in case  of unique solution ratio of coefficient is as follows,

$\frac{a_1}{a_2}\neq\frac{b_1}{b_2}$

So, we get

$\frac{k}{3}\neq\frac{2}{6}$

$k\neq\frac{2}{6}\times3$

k ≠ 1

Therefore, Value of k is all integers other than 1.