Question

Find the value of x for lich the system of equations
4r + 5y = 0
kr + 10y = 0 has infinitely many solutions.​

Answer 1

For all real values k other than 6 , the system of equations has non zero solution.

Step-by-step explanation:

Given system of equations:

3x+5y=0 ,

kx+10=0 ,

Compare this with a1x+b1y+c1=0

and

a2x+b2y+c2 = 0, we get

a1 = 3 , b1 = 5, c1 = 0

a2 = k , b2= 10, c2=0

The equations have non zero solution,

Here ,

a1b2-a2b1≠0

=> 3×10-k×5 ≠ 0

=> 30 - 5k ≠ 0

=> -5k ≠-30

On dividing each term by -5, we get

=> k ≠ 6

If plot the lines ,we will notice that they are parallel.

So, for this problem to have non -zero solution , k is any real number other than 6.

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Answer 2

Correct question:

Find the value of k for which the system of equations

4x + 5y = 0

kx + 10y = 0 has infinitely many solutions.

Solution:

The given system is of the form

a1x + b1y = 0

a2x + b2y = 0

a1 = 4 , b1 = 5

a2 = k , b2 = 10

if a1/a2 = b1/b2 ,the system has infinitely many solutions.

⇒ 4/k = 5/10

⇒5 × k = 4 × 10

⇒ k = 40/5

⇒ k = 8