Question

find value of k for which the pair of linear 5x+2y = k and 10 x + 4y = 3 has many infinite solution​

Answer 1

⠀⠀⠀⠀⠀⠀According to the Question

• 1st equation = 5x + 2y = k
• 2nd equation = 10x + 4y = 3

where,

• a1 = 5 , b1 = 2 , c1 = k

• a2 = 10 , b2 = 4 , c2 = 3

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It is given that the linear equation has infinitely many solution . So , the condition necessary for infinitely many solution is

• a1/a2 = b1/b2 = c1/c2

Substitute the value we get

$:\implies$ 5/10 = 2/4 = k/3

$:\implies$ 1/2 = 1/2 = k/3

$:\implies$ 1/2 = 1/2 or 1/2 = k/3

$:\implies$ 1/2 = k/3

$:\implies$ 2k = 3

$:\implies$ k = 3/2

• Hence, the value of k is 3/2 .

Answer 2

Question

find value of k for which the pair of linear

5x+2y = k and 10 x + 4y = 3 has many infinite

solution.

According to the question

• We have to find the value of (k)

• But main problem is that 3 have many infinite solution.

Formula

A1/A2 = B1/ B2 = C1/C2

5/10=2/4= k3

½=½=k/3

½=½ or ½ = k3

½ = k/3

2k = 3

k= 3/2

Proved k= 3/2