Ex.4.3 Q2 Linear Equations in Two Variables Solution - NCERT Maths Class 9
Given the equations of two lines passing through \((2, 14).\) How many more such lines are there, and why?
What is known?
Point (\(2, 14\)) at which line passes through
What is Unknown?
Equation of line and number of lines which can passes through the given point.
We can think for those equations which could satisfy the given point.
It can be observed that point \((2, 14)\) satisfies the equation \(7x − y = 0\) and \(x − y + 12 = 0\).
Therefore, \(7x − y = 0\) and \(x − y + 12 = 0\)
are two lines passing through point \((2, 14).\)
As it is known that through one point, infinite number of lines can pass through, therefore, there are infinite lines of such type passing through the given point.