Use graph paper for this question. Draw the graph of 2x - y - 1 = 0 and 2x + y = 9 on the same axes. Use 2 cm = 1 unit on both axes and plot only 3 points per line.

Write down the co-ordinates of the point of intersection of the two lines.

First equation: 2x - y - 1 = 0

Step 1:

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

Let x = 0, then 2 $\times$ 0 - y - 1 = 0 ⇒ y = -1

Let x = 2, then 2 $\times$ 2 - y - 1 = 0 ⇒ y = 3

Let x = 4, then 2 $\times$ 4 - y - 1 = 0 ⇒ y = 7

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: 2x + y = 9

Step 1:

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

Let x = 0, then 2 $\times$ 0 + y = 9 ⇒ y = 9

Let x = 2, then 2 $\times$ 2 + y = 9 ⇒ y = 5

Let x = 4, then 2 $\times$ 4 + y = 9 ⇒ 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.

On the same graph paper, draw the graph for each given equation.

Both the straight line drawn meet the point P. As it is clear from the graph, co - ordinate of the common point P are (2.5, 4).

Solution of the given equation x = 2.5 and y = 4.

Hence, point of intersection = (2.5, 4).