Question

Find the value of k for which each of the following systems of equations have infinitely many solution:
8x+5y=9kx+10y=18

Answer 1

• The value of k for which the given system of equations have infinitely many solutions 8x+5y=9
• let this be equation (1)

• kx+10y=18 let this be equation (2)

• The above equations are of the form a₁x+b₁y=c₁ and a₂x+b₂y=c₂

• From the general equations we get the values of a₁, b₁, c₁ and a₂, b₂, c₂
• They are a₁=8, b₁=5, c₁=9 and a₂=k, b₂=10, c₂=18
• For equations having infinitely many solutions the condition is a₁/a₂=b₁/b₂=c₁/c₂
• That is 8/k=5/10=9/18
• As the denominator is 2×numerator, k will be 2×8=16
• k=16

Answer 2

For system of equation have infinite many solution , the value of k is 16

Step-by-step explanation:

Given as :

The linear equation are

8 x + 5 y - 9  = 0                        .........1

k x + 10 y - 18 = 0                      ........2

The standard equation

$a_1 x + b_1 y + c_1 = 0$

$a_2 x + b_2 y + c_2$ = 0

The system of equation have infinite many solution

The condition for infinite many solution

$\dfrac{a_1}{a_2} = \dfrac{a_2}{b_2} = \dfrac{c_1}{c_2}$

$\dfrac{8}{k} = \dfrac{5}{10} = \dfrac{9}{18}$

by cross multiplication

8 × 10 = 5 × k

∴ k = $\dfrac{80}{5}$

i.e  k = 16

So, The value of k = 16

Hence, for system of equation have infinite many solution , the value of k is 16 Answer