Question

Draw the graph for each of the equation 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

$$\begin{gathered} x+y=6 \\ \Rightarrow y=-x+6 \end{gathered}$$
When x = 0, $y=-0+6=6$
When x = 1, $y=-1+6=5$
When x = 3, $y=-3+6=3$

Thus, the points on the line x + y = 6 are as given in the following table:

x	0	1	3
y	6	5	3

Plotting the points (0, 6), (1, 5) and (3, 3) and drawing a line passing through these points, we obtain the graph of of the line x + y = 6.

$$\begin{gathered} x-y=2 \\ \Rightarrow y=x-2 \end{gathered}$$
When x = 0, $y=0-2=-2$
When x = 2, $y=2-2=0$
When x = –1, $y=-1-2=-3$

Thus, the points on the line x – y = 2 are as given in the following table:

x	0	2	–1
y	–2	0	–3

Plotting the points (0, –2), (2, 0) and (–1, –3) and drawing a line passing through these points, we obtain the graph of of the line x – y = 2.



It can be seen that the lines x + y = 6 and x – y = 2 intersect at the point (4, 2).