Question

For what values of k , the following system of equations has infinitely many solutions: k x + 5 y – ( k – 5) = 0 20 x + k y – k = 0

Answer 1

Answer:

the value of k is 10 in both the equations

Step-by-step explanation:

here for infinite solutions a1/a2 = b1/b2 = c1/c2

here k/20 = 5/k = k-5/k

I) k/20 = 5/k

k×k = 20×5

{k}^{2} = 100k

2

=100

k=√100

thus k= 10

ii) k/20 = (k-5)/k

k×k = 20×(k-5)

{k}^{2} = 20k - 100k

2

=20k−100

{k}^{2} - 20k = - 100k

2

−20k=−100

k(k - 20) = - 100k(k−20)=−100

k= 10

k - 20 = 100 \div 10k−20=100÷10

k - 20 = - 10k−20=−10

\begin{gathered}k = - 10 + 20 \\ k = 10\end{gathered}

k=−10+20

k=10

therefore the value of k is 10 in both the equations