Question

Find 'k' if the following pair of linear equations has no solution:
2x + y = 3; x+ (k-1)y= 7​

Answer 1

Answer:

3/2

Step-by-step explanation:

If there is no solution, then

(a₁/a₂) = (b₁/b₂) ≠ (c₁/c₂)

Here,

a₁=2, b₁=1, c₁=3

a₂=1, b₂=k-1, c₂=7

2/1 = 1/(k-1) ≠ 3/7

2/1 = 1/(k-1)

⇒2k-2 = 1

⇒2k = 3

⇒k = 3/2

Answer 2

Answer:

$2x + y = 3 \\ x +(k - 1)y = 7$

Step-by-step explanation:

$\frac{a1}{a2} = \frac{b1}{b2} = \frac{c1}{c2}$

$\frac{2}{1} = \frac{1}{k - 1} = \frac{3}{7}$

$\frac{a1}{a2} = \frac{b1}{b2}$

$\frac{2}{1} = \frac{1}{k - 1}$

$2k - 2 = 1$

2k=1+2

2k=3

$k = \frac{3}{2}$

and

$\frac{b1}{b2} = \frac{c1}{c2}$

$\frac{1}{k - 1} = \frac{3}{7}$

3k - 3 = 7

3k = 7+3

3k = 10

$k = \frac{10}{3}$

$k = \frac{3}{2} \: or \: \frac{10}{3}$