Question

Find the value of K if equation have many solution
Solutions kx-5y=3 , 8x-10y=6
​

Answer 1

AnsWer :

k = 4.

GiveN :

• kx - 5x = 3.
• 8x - 10y = 6.
• Have Many Solution / Infinite many solution.

SolutioN :

We have, Pair of Linear Equation.

$\tt \dagger \: \: \: \: \: kx - 5x = 3.$ $\tt \dagger \: \: \: \: \: 8x - 10y = 6.$

Where as,

• a1 = k.
• a2 = 8.
• b1 = - 5.
• b2 = - 10.
• c1 = 3.
• c2 = 6.

★ Now, given [ Many Solution ]

$\tt \dagger \: \: \: \: \: \dfrac{a_1}{ a_2} = \dfrac{b_1}{ b_2} = \dfrac{c_1}{ c_2}$

$\tt : \implies \dfrac{k}{8} = \dfrac{ - 5}{ - 10} = \dfrac{3}{6}$

$\tt : \implies \dfrac{k}{8} = \dfrac{ - 5}{ - 10}$

$\tt : \implies \dfrac{k}{8} = \dfrac{ \cancel{- 5}}{ \cancel{- 10}}$

$\tt : \implies \dfrac{k}{8} = \dfrac{ 1}{ 2}$

$\tt : \implies k = 4.$

And,

$\tt : \implies \dfrac{k}{8} = \dfrac{3}{6}$

$\tt : \implies \dfrac{k}{8} = \dfrac{ \cancel3}{ \cancel6}$

$\tt : \implies k = 4.$

Therefore, the value of k = 4.