Question

find the value of k for which the system of equation have infinitely many solutions x-ky=2, 3x+6y=-5full solution

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Answer 1

Answer:

-18 or 15 is the required value of k .

Step-by-step explanation:

According to the Question

It is given that the equation has infinitely many solution .

1st Equation = x-ky=2

➻ 1 equation = x -ky-2 = 0

where, a₁ = 1 , b₁ = -k & c₁ = -2

2nd equation = 3x + 6y = -5

➻ 2nd equation = 3x+6y+5 = 0

where,

a₂ = 3 , b₂ = 6 & c₂ = 5

as we know the condition for the equation which have infinitely many solution.

• a₁/a₂ = b₁/b₂ = c₁/c₂

Putting all the value we get

➻ 1/3 = -k/6 = -2/5

➻ 1/3 = -k/6 or -k/6 = -2/5

➻ -k = 18 or 2k = 30

➻ k = -18 or k = 30/2

➻ k = -18 or k = 15

• Hence, the value of k is -18 or 15 respectively.

Answer 2

Answer:

$\underline{\purple{\ddot{\Mathsdude}}}$

♧♧To prove :-

• The value of k for the given system.

♧♧Explanation: -

• Here already given that the system of equation have infinitely Many solutions.

Lets take,

1. First equation= x-ky=2.

• where a = 1 , b=-k, c= -2

2. Second equation = 3x+6y =-5

• where a = 3 , b=6, c= +5.

♧We have already know the formula of infinitely many solutions is

●a1/a2:b1/b2:c1/c2

☆☆Now putting the values in formula :-

• 1/3=-k/6=-2/5
• 1/3=-k/6 or -k/6=-2/5

1. -k=18 or 2k = 30

• k=-18 or k= 30/2
• k=-18 or k=15.

☆Therefore, the values of k is -18 and 15.

♧♧Hope it helps u mate .

♧♧Thank you.