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Question
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.
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Solution
2y - x = 8;
y = `(8 + x)/(2);`
The table of 2y - x = 8 is
| X | - 6 | - 2 | 0 |
| Y | 1 | 3 | 4 |
5y - x = 14
⇒ x = 5y - 14
The table of x = 5y - 14 is
| X | - 9 | - 4 | 1 |
| Y | 1 | 2 | 3 |
y - 2x = 1
⇒ y = 1 + 2x
The table of y - 2x = 1 is
| X | 2 | - 2 | 0 |
| Y | 5 | - 3 | 1 |
Now plotting the points on a graph and we get the following required graph:
Thus, the verticles of the triangle ΔABC are: A(- 4, 2), B(1, 3) and C(2, 5).
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