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Question
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?
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Solution
2x + 3y = 4
⇒ x = `(4 - 3y)/(2)`
The table for 2x + 3y = 4 is
| X | -1 | -4 | 5 |
| Y | 2 | 4 | -2 |
x - y = 7
⇒ x = y + 7
The table for x - y = 7 is
| X | 5 | 11 | 9 |
| Y | -2 | 4 | 2 |
Now plot the points on a graph and we get the following required graph:
The point at which the paths of the submarine and the destroyer intersect are (5, -2)
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