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Question
Solve the following equations graphically :
2x - y = 9
5x + 2y = 27
Solution
2x - y = 9
5x + 2y = 27
2x - y = 9 _________(1)
5x + 2y = 27 ________(2)
Now, 2x - y = 9
⇒ y = 2x - 9
Corresponding values of x and y can be tabulated as :
| x | 2 | 3 | 4 |
| y | -5 | -3 | -1 |
Plotting points (2, -5), (3, -3), (4, -1) and joining them, we get a line l, which is the graph pf equation (1).
Again, 5x + 2y = 27
⇒ y = `(27 - 5x)/(2)`
Corresponding values of x and y can be tabulated as :
| x | 5 | 4 | 3 |
| y | 1 | 3.5 | 6 |
Plotting points (5, 1), (4, 3.5), (3, 6) and joining them, we get a line l2 which is the graph of equation (2).
The two lines l1 and l2 intersect at a unique point (5, 1).
Thus, x = 5 and y = 1 is the unique solution of the given equations.
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