Question

Draw the graphs for the equations x + y = 6 and x − y = 2 on the same graph paper and find the coordinates of the point where the two straight lines intersect.

Answer 1

The equations are $x+y=6$ and $x-y=2$.
Now, consider $x+y=6$.
When $x=0$, then $y=6$.
When $x=2$, then $y=4$.
When $x=6$, then $y=0$.

Thus, we get the following table:

$\text{x}$	0	2	6
$y$	6	4	0

Plot the points $(0,6),(2,4)$ and $(6,0)$ on the graph paper. Then, join the points and extend them in both the directions.
Now, consider $x-y=2$.
When $x=0$, then $y=-2$.
When $x=1,$ then $y=-1$.
When $x=2$, then $y=0$.

Thus, we get the following table:

$\text{x}$	0	1	2
$y$	-2	-1	0

Plot these points on the graph paper. Then, join the points and extend them in both the directions.



From the graph, we can see that the two lines intersect at (4,2) .