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प्रश्न
Use the graphical method to show that the straight lines given by the equations x + y = 2, x - 2y = 5 and `x/(3) + y = 0` pass through the same point.
उत्तर
The equations can be written as follows:
y = 2 - x
y = `(1)/(2)(x - 5)`
y = `- x/(3)`
First prepare a table as follows:
| X | Y = 2 - x | Y = `(1)/(2)(x - 5)` | Y = `-x/(3)` |
| - 1 | 3 | - 3 | `(1)/(3)` |
| 0 | 2 | `-(5)/(2)` | 0 |
| 1 | 1 | - 2 | `-(1)/(3)` |
Thus the graph can be drawn as follows:
From the graph it is clear that the equation of lines are passes through the same point.
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संबंधित प्रश्न
Draw the graphs of the following equations on the same system of co-ordinates. Write the co-ordinates of their points of intersection.
x + 4 = 0, y - 1 = 0, 2x + 3 = 0, 3y - 15 = 0
Draw the graph for the linear equation given below:
y = - 2x
Draw the graph for the linear equation given below:
y = `(2x)/(3) - 1`
Draw the graph for the linear equation given below:
x - 3 = `(2)/(5)(y + 1)`
For the linear equation, given above, draw the graph and then use the graph drawn (in the following case) to find the area of a triangle enclosed by the graph and the co-ordinates axes:
3x - (5 - y) = 7
Draw a graph of each of the following equations: x + 6y = 15
Draw a graph of each of the following equations: x + y - 3 = 0
Draw a graph for each of the following equations and find the coordinates of the points where the line drawn meets the x-axis and y-axis: `(2x)/(5) + y/(2)` = 1
Draw a graph of the equation 2x + 3y + 5 = 0, from the graph find the value of:
(i) x, when y = -3
(ii) y, when x = 8
Draw the graph of the lines represented by the equations 3x - 2y = 4 and x + y = 3 on the same graph. Find the coordinates of the point where they intersect. State, whether the lines are perpendicular to each other.
