One of the most important and conceptual question from linear equations in two variables in which we have given two equations 3x+5y=0, kx+10y=0 and we need to calculate the value of k for which the given equations have a nonzero solution
RS Aggarwal, Class 10, chapter 3F, question no 16
For a system of equations a1x+b1y+c1=0; a2x+b2y+c2=0 to have non-zero solutions, the condition to be satisfied is
a1/a2=b1/b2=c1/c2
∴3/k=5/10
or k=6