Question

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

Answer 1

Table of eq1

$x$	1	2	3
$y$	2	1	0

Table of eq2

$x$	1	2	3
$y$	2	1	0

The given equation can be written as
$x+y-3=0$ .......eq1 and $3x+3y-9=0$ .........eq2
Here, $\frac{a_1}{a_2}=\frac{1}{3},\frac{b_1}{b_2}=\frac{1}{3},\frac{c_1}{c_2}=\frac{3}{9}=\frac{1}{3}$
$\therefore \frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$
Thus, the given pair of equation is consistent.