Question

Write an equation of a line passing through the point representing solution of the pair of linear equations $x+y=2\mathrm{and}2x-y=1$. How many such lines can we find ?

Answer 1

The given equations are
$$\begin{gathered} x+y=2.....\left(\mathrm{i}\right) \\ 2x-y=1.....\left(\mathrm{ii}\right) \end{gathered}$$
Adding (i) and (ii), we get
3x = 3
⇒ x = 1
Putting x = 1 in (i), we get
1 + y = 2
⇒ y = 1
Thus, the solution of the given equations is (1, 1).
We know that, infinitely many straight lines pass through a single point.
So, the equation of one such line can be 3x + 2y = 5 or 2x + 3y = 5.