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Question
Solve the following system of equations graphically
x - y + 1 = 0
4x + 3y = 24
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Solution
x - y + 1 = 0 ...(1)
4x + 3y = 24 ...(2)
x - y + 1 = 0
⇒ y = x + 1
Corresponding values of x and y can be tabulated as :
| x | 0 | 3 | -1 |
| y | 1 | 4 | 0 |
Plotting points (0, 1), (1, 2), (-1, 0) and joining them, we get a line l1 which is the graph of equation (1).
4x + 3y = 24
⇒ x = `(24 - 3y)/(4)`
Corresponding values of x and y can be tabulated as :
| x | 6 | 3 | 0 |
| y | 0 | 4 | 8 |
Plotting points (6, 0), (3, 4), (0, 8) and joining them, we get a line l2 which is the graph of equation (2).
The lines l1 and l2 intersect at (3, 4). Thus, x = 3 and y = 4 is the unique solution of equation (1) and (2).
Now, from the graph, it can be seen that the lines l1, and l2
Intersect the x-axis at points (-1, 0) and (6, 0).
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