Question

Find the value of ‘k’ for which the system of equations kx− 5y = 2; 6x+ 2y = 7

has no solution.​

Answer 1

Given:-

Pair of equations kx-5y=2 and 6x+2y = 7

To Find:-

Value of k such that the given pair of equations has no solution.

Solution:-

We know that for two equations to have no solution

$\frac{a1}{a2} = \frac{b1}{b2} not \: equal \: to \: \frac{c1}{c2}$

We have,

a1 = k

a2 = 6

b1 = -5

b2 = 2

c1 = 2 and c2 = 7

Put the value of variables in the above equation, we get,

$\frac{k}{6} = \frac{ - 5}{2 \:} not \: equal \: to \: \frac{2}{7}$

In first case,

$\frac{k}{6} = \frac{ - 5}{2}$

$= > 2k = - 30$

$= > k = - 15$

Now in second case,

$\frac{k}{6} not \: equal \: to \: \frac{2}{7}$

Solving the equation, we get,

$k \: is \: not \: equal \: to \frac{12}{7}$

Hence, the value of k is not equal to 12/7