Draw the graph of the equation `x+y = 3 and y -x =1`. What do you observe ?

Explanation

(a) `x +y =3`
`{:(x,,-2,,-1,,0,,1,,2),(y=3-x,,5,,4,,3,,2,,1):}`
`therefore` Some of the ordered pairs which satisfy the equation `x +y = 3` are `(-2, 5), (-1, 4), (0, 3), (1, 2), (2, 1)`.
(b) `y -x =1`
`{:(x,,-2,,-1,,0,,1,,2),(y=1+x,,-1,,0,,1,,2,,3):}`
`therefore` Some of the ordered pairs which satisfy the equation `y-x =1` are (-2, -1), (-1, 0), (0, 1), (1, 2), (2, 3).
By plotting the above points the above points on the graph sheet, we get the following graph.

From the above graph, we notice that the two given equations are intersecting at teh point (1, 2). i.e., `x +y =3 and y -x =1` have a common point `(1, 2)`. Therefore, (1, 2) is the solution of the equation `x+y =3 and y-x=1`.
Verification
`x +y = 3 to (1)`
`y-x=1 to (2)`
By adding (1) and (2), we get,
`y = 2 rArr x =1`
`therefore (1, 2)` is the solution of `x+y =3 and y -x =1`.