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प्रश्न
Solve the following equations graphically :
x = 4
`(3x)/(3) - y = 5`
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उत्तर
x = 4
`(3x)/(3) - y = 5`
x = 4 ________(1)
`(3x)/(3) - y = 5` _________(2)
The graph of equation (1) will be the line l1 which is at a distance of 4 units from the y-axis. (4, 0)
From (2), x - y = 5
Corresponding values of x and y can be tabulated as :
| x | 4 | 0 | 5 |
| y | - | -5 | 0 |
Plotting points (4, -1), (0, -5), (5, 0) and joining them, we get a line l2 which is the graph of equation (2).
The two lines l1 and 12 intersect at a unique point (4, -1). Thus, x = 4 and y = 1 -1 is the unique solution of the given equations.
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संबंधित प्रश्न
The cost of manufacturing x articles is Rs. (50 + 3x). The selling price of x articles is Rs. 4x.
On a graph sheet, with the same axes, and taking suitable scales draw two graphs, first for the cost of manufacturing against no. of articles and the second for the selling price against the number of articles.
Use your graph to determine:
No. of articles to be manufactured and sold to break even (no profit and no loss).
The cost of manufacturing x articles is Rs.(50 + 3x). The selling price of x articles is Rs. 4x.
On a graph sheet, with the same axes, and taking suitable scales draw two graphs, first for the cost of manufacturing against no. of articles and the second for the selling price against the number of articles.
Use your graph to determine:
The profit or loss made when (a) 30 (b) 60 articles are manufactured and sold.
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.
Solve graphically, the following equations.
x + 2y = 4; 3x - 2y = 4.
Take 2 cm = 1 unit on each axis.
Also, find the area of the triangle formed by the lines and the x-axis.
Solve the following equations graphically :
3y = 5 - x
2x = y + 3
Solve the following equations graphically :
x - 2y = 2
`x/(2) - y` = 1
Find graphically the vertices of the triangle, whose sides have the equations 2y - x = 8, 5y -x = 14 and y = 2x - 1.
Draw the graph of the following equations :
3x + 2y + 6 = 0
3x + 8y - 12 = 0
Also, determine the co-ordinates of the vertices of the triangle formed by these lines and x-axis.
Solve graphically
x – y = 0, y + 3 = 0
Solve graphically
x = −3, y = 3
