The value of k for which the system of equations 3x + 5y = 0 and kx + 10y = 0 has a non-zero solution, is
Given:
Equation 1: 3x + 5y = 0
Equation 2: kx + 10y = 0
Both the equations are in the form of :
a1x + b1y = c1 & a2x + b2y = c2 where
a1 & a2 are the coefficients of x
b1 & b2 are the coefficients of y
c1 & c2 are the constants
According to the problem:
a1 = 3
a2 = k
b1 = 5
b2 = 10
c1 = 0
c2 = 0
The equation will have a non zero solution only when it will satisfy a non trivial solution i.e. the equations should satisfy with values other than x = 0 & y = 0 .For the given system of equations the equation will have a non zero solution if
.......(i)
Putting the above values in equation (i) we get: