Question

The value of k for which the following system of linear equations represent coincident lines is 2x + 9y = k; 8x + 36y = 4

Answer 1

Answer:

k = 1

Step-by-step explanation:

equation 1 --> 2x + 9y = k

                      2x + 9y - k = 0

coefficients are -> a1 = 2 , b1 = 9, c1 = -k

equation 2 --> 8x + 36y = 4

                      8x + 36y - 4 = 0

coefficients are -> a2 = 8 , b2 = 36, c2 = -4

for coincident lines

$\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}\\putting \ values\\\frac{2}{8} = \frac{9}{36} = \frac{-k}{-4}\\\\\frac{1}{4} = \frac{1}{4} = \frac{k}{4}\\\\therefore \ k = 1$

value of k = 1