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

Given:

Given pair of linear equations is $x + y = 2$ and $2x - y = 1$. 

To do:

We have to write an equation of a line passing through the point representing solution of the given pair of linear equations. 

Solution:

$x+y=2$

$y=2-x$...(i)

Substituting $y=2-x$ in $2x - y = 1$, we get,

$2x-(2-x)=1$

$2x-2+x=1$

$3x=2+1$

$3x=3$

$x=\frac{3}{3}$

$x=1$  

Substituting $x=1$ in $y=2-x$, we get,

$y=2-1$

$y=1$

Therefore, the solution of the given pair of equations is $(x, y)=(1, 1)$.

We know that,

There are infinite lines passing through a point $(x, y)$.

Therefore, there are infinite lines passing through the solution of the given pair of equations $(1, 1)$.

The general form of a linear equation in two variables is $ax+by+c=0$.

An equation of a line passing through the point representing solution of the pair of linear equations $x + y = 2$ and $2x - y = 1$ is $4x-y=3$.