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Question
By drawing a graph for each of the equations 3x + y + 5 = 0; 3y - x = 5 and 2x + 5y = 1 on the same graph paper; show that the lines given by these equations are concurrent (i.e. they pass through the same point). Take 2 cm = 1 unit on both the axes.
Solution
3x + y + 5 = 0
⇒ y = - 3x - 5
The table of 3x + y + 5 = 0 is
| X | 1 | - 3 | - 2 |
| Y | - 8 | 4 | 1 |
3y - x = 5
⇒ x = 3y - 5
The table of 3y - x = 5 is
| X | - 2 | 1 | 7 |
| Y | 1 | 2 | 4 |
2x + 5y = 1
⇒ 2x = 1 - 5y
⇒ x = `(1 - 5y)/(2)`
The table of 2x + 5y = 1 is
| X | 3 | - 7 | - 2 |
| Y | - 1 | 3 | 1 |
Plotting the above points, we get the following required graph:
The graph shows that the lines of these equations are concurrent.
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