Question

For the for the following pair of linear equation write down the condition of parallel line and also find the value of k
2x + 3y = 7
(k - 1)x +(3k - 2)y = 6k + 2​

Answer 1

Answer:

I don't understand your question

Answer 2

Answer:

7

Step-by-step explanation:

The given system of equations:

2x + 3y = 7,

2x + 3y - 7 = 0.... (i) And, (k-1)x+ (k + 2)y = 3k

→ (k-1)x+ (k+ 2)y - 3k = 0

These equations are of the following form:

a₁2b₁y+c₁= 0, a₂x + b₂y + C₂ = 0

where,

a1 =

2, b₁

= 3, C1

= -7 and a2

(k-1), b₂ =

For an infinite number of solutions, we must

have:

a1

b₁

C1

(c b₂ 1) 2 3 (k+2) -7 -3k

2 (k-1) 3 (k+2) 7 3k Now, we have the following three cases:

Case I: 2

3

(k-1) k+2 → 2(k+ 2) = 3(k-1) 2k + 4 = 3k-3 = k = 7

Case II: 3

7

(k+2) - 3k 7(k+ 2) = 9k→ 7k+ 14 = 9k 2k = 14 → k = 7 Case III:

2 -

7

(k-1) → 7k - 7 = 6k → k = 7 Hence, the given system of equations has an

infinite number of solutions when k is equal to 7.