The course of an enemy submarine, as plotted on rectangular co-ordinate axes, gives the equation 2x + 3y = 4. On the same axes, a destroyer's course is indicated by the graph x - y = 7. Use the graphical method to find the point at which the paths of the submarine and the destroyer intersect.

Enemy equation: 2x + 3y = 4

Step 1:

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

Let x = -4, then 2 $\times$ (-4) + 3y = 4 ⇒ y = 4

Let x = -1, then 2 $\times$ (-1) + 3y = 4 ⇒ y = 2

Let x = 5, then 2 $\times$ 5 + 3y = 4 ⇒ y = -2

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.

Destroyer equation: x - y = 7

Step 1:

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

Let x = 5, then 5 - y = 7 ⇒ y = -2

Let x = 9, then 9 - y = 7 ⇒ y = 2

Let x = 11, then 11 - y = 7 ⇒ y = 4

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.

Both the straight lines intersect at point P. As it is clear from the graph, co-ordinates of point P are (5, -2).

Hence, (5, -2) is the point at which the paths of the submarine and the destroyer intersect.