Find graphically, the vertices of the triangle whose sides have the equations 2y - x = 8; 5y - x = 14 and y - 2x = 1 respectively.

Take 1 cm = 1 unit on both the axes.

First equation: 2y - x = 8

Step 1:

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

Let x = -4, then 2y - (-4) = 8 ⇒ y = 2

Let x = -2, then 2y - (-2) = 8 ⇒ y = 3

Let x = 0, then 2y - 0 = 8 ⇒ y = 4

Let x = 2, then 2y - 2 = 8 ⇒ y = 5

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: 5y - x = 14

Step 1:

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

Let x = -4, then 5y - (-4) = 14 ⇒ y = 2

Let x = 0, then 5y - 0 = 14 ⇒ y = 2.8

Let x = 2, then 5y - 2 = 14 ⇒ y = 3.2

Let x = 4, then 5y - 4 = 14 ⇒ y = 3.6

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: y - 2x = 1

Step 1:

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

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

Let x = 2, then y - 2 $\times$ 2 = 1 ⇒ y = 5

Let x = 4, then y - 2 $\times$ 4 = 1 ⇒ y = 9

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.

The vertices of the triangle are:

The coordinate of A = (2, 5)

The coordinate of B = (-4, 2)

The coordinate of C = (1, 3)

Hence, the coordinates of the vertices of triangle = (1, 3), (-4, 2) and (2, 5).