Question

Solve the following pair of equations graphically.
$x+y=4;x=y$

Answer 1

$x+y=4$
$\Rightarrow y=4-x$ ......(i)
when $x=1,y=4-1=3$
when $x=2,y=4-2=2$
when $x=3,y=4-3=1$
when $x=4,y=4-4=0$
$x=1,2,3,4$

$y=3,2,1,0$
Plot the above ordered pairs $(1,3),(2,2),(3,1)$ and $(4,0)$ on the graph paper, join them and get the graph AB (Line segment) and $x=y$
when $x=0,y=0$
$x=1,y=1$
$x=2,y=2$
$x=3,y=3$
$x=0,1,2,3$

$y=0,1,2,3$
Plot the points $(1,1),(2,2),(0,0)$ and $(3,3)$ on the same graph paper, join them and the get graph CD
The point of intersection of AB and CD is $(2,2)$
Hence, required solution is $x=2,y=2.$