By the graphical method, find whether the following pair of equations are consistent or not. If consistent, solve them.
$ x+y=3 $
$ 3 x+3 y=9 $

AcademicMathematicsNCERTClass 10


Pair of linear equations:

\( x+y=3 \)

\( 3 x+3 y=9 \)

To do:

We have to find whether the given pair of linear equations is consistent /inconsistent. If consistent, then obtain the solution graphically.





$a_{1}=1, b_{1}=1, c_{1}=-3$

$a_{2}=3, b_{2}=3, c_{2}=-9$





$\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}}=\frac{c_1}{c_2}$

This implies,

The given pair of lines is coincident and therefore consistent.

For equation (i),



Plot point $( 0,\ 3)$ and $(3,\ 0)$ on a graph and join then to get equation $x+y=3$

For equation (ii), 




Plot points $(0,\ 3)$ and $(3,\ 0)$ on a graph and join them to get equation $3x+3y=9$

There are infinite solutions as the lines are coincident.

Updated on 10-Oct-2022 13:27:19