Use the graphical method to show that the straight lines given by the equations $x + y = 2, x - 2y = 5$ and $\dfrac{x}{3} + y = 0$ pass through the same point.

First equation : x + y = 2

Step 1:

Give at least three suitable values to the variable x and find the corresponding values of y.

Let x = -1, then (-1) + y = 2 ⇒ y = 3

Let x = 0, then 0 + y = 2 ⇒ y = 2

Let x = 1, then 1 + y = 2 ⇒ y = 1

Let x = 3, then 3 + y = 2 ⇒ y = -1

Step 2:

Make a table (as given below) for the different pairs of the values of x and y:

Step 3:

Plot the points, from the table, on a graph paper and then draw a straight line passing through the points plotted on the graph.

Second equation : x - 2y = 5

Step 1:

Give at least three suitable values to the variable x and find the corresponding values of y.

Let x = -1, then (-1) - 2y = 5 ⇒ y = -3

Let x = 0, then 0 - 2y = 5 ⇒ y = -2.5

Let x = 1, then 1 - 2y = 5 ⇒ y = -2

Let x = 3, then 3 - 2y = 5 ⇒ y = -1

Step 2:

Make a table (as given below) for the different pairs of the values of x and y:

Step 3:

Plot the points, from the table, on a graph paper and then draw a straight line passing through the points plotted on the graph.

Third equation : $\dfrac{x}{3} + y = 0$

Step 1:

Give at least three suitable values to the variable x and find the corresponding values of y.

Let x = -3, then $\dfrac{-3}{3} + y = 0$ ⇒ y = 1

Let x = 0, then $\dfrac{0}{3} + y = 0$ ⇒ y = 0

Let x = 3, then $\dfrac{3}{3} + y = 0$ ⇒ y = -1

Step 2:

Make a table (as given below) for the different pairs of the values of x and y:

Step 3:

Plot the points, from the table, on a graph paper and then draw a straight line passing through the points plotted on the graph.

Hence, the three straight lines pass through the same point.