Question

Find the value of k for which the system of equations
3x - y = 5, 6x - 2y = k
has no solution

Answer 1

The given system of equations:
3x - y - 5 = 0                      ….(i)
And, 6x - 2y + k = 0             ….(ii)
These equations are of the following form:
`a_1x+b_1y+c_1 = 0, a_2x+b_2y+c_2 = 0`
where,`a_1 = 3, b_1= -1, c_1= -5 and a_2 = 6, b_2= -2, c_2 = k`
In order that the given system has no solution, we must have:
`(a_1)/(a_2) = (b_1)/(b_2) ≠ (c_1)/(c_2)`
` i.e., 3/6 = (−1)/(−2) ≠ −5/k`
`⇒(−1)/(−2) ≠ (−5)/k ⇒ k ≠ -10`
Hence, equations (i) and (ii) will have no solution if k ≠ -10.