Question

Find the value of k for which the system of equations 2x + 3y -5 = 0 and 4x + ky – 10 = 0 has infinite number of solutions.

Answer 1

The given system is
2x + 3y – 5 = 0                         ……(i)
4x + ky – 10 = 0                    ……(ii)
Here,` a_1 = 2, b_1 = 3, c_1 = -5, a_2 = 4, b_2 = k and c_2 = -10`
For the system, to have an infinite number of solutions, we must have
`(a_1)/(a_2) = (b_1)/(b_2) = (c_1)/(c_2)`
`⇒ 2/4 = 3/k = (−5)/(−10)`
`⇒ 1/2 = 3/k= 1/2`
⇒ k = 6
Hence, k = 6.