An important and exam oriented question from linear equations in two variables in which we have given two equations 2x-3y=5, 6x-9y=15 and we have to show that these equations have infinite number of solutions
RS Aggarwal, Class 10, chapter 3D, question no 10
2x−3y=5,6x−9y=15
Here,
a1=2, b1=−3, c1=5
a2=6, b2=−9, c2=15
a1/a2=2/6=1/3, b1/b2=−3/−39=1/3
and
a1/a2=b1/b2=c1/c2
This system has an infinity number of solution.