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Question
Solve the following equations graphically :
x + 3y = 8
3x = 2 + 2y
Solution
x + 3y = 8
3x = 2 + 2y
x + 3y = 8 ________(1)
3x = 2 + 2y _______(2)
Now, x + 3y = 8
⇒ y = `(8 - x)/(3)`
Corresponding values of x and y can be tabulated as :
| x | -1 | 2 | 5 |
| y | 3 | 2 | 1 |
Plotting points (-1, 3), (2, 2), (5, 1) and joiniing them, we get a line I, which is the graph of equation (1).
Again, 3x = 2 + 2y
⇒ x = `(2x + 2y)/(3)`
Corresponding values of x and y can be tabulated as :
| x | 2 | 4 | 0 |
| y | 2 | 5 | -1 |
Plotting points (2, 2), (4, 5), (0, -1) and joining them, we get a line I2 which is the graph of equation (2).
The two lines I2 and I2 intersect at the point (2, 2). Hence, x = 2, y = 2 is the unique solution of the given equation.
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