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प्रश्न
The course of an enemy submarine, as plotted on rectangular co-ordinate axes, gives the equation 2x + 3y = 4. On the same axes, a destroyer's course is indicated by the graph x - y = 7. Use the graphical method to find the point at which the paths of the submarine and the destroyer intersect?
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उत्तर
2x + 3y = 4
⇒ x = `(4 - 3y)/(2)`
The table for 2x + 3y = 4 is
| X | -1 | -4 | 5 |
| Y | 2 | 4 | -2 |
x - y = 7
⇒ x = y + 7
The table for x - y = 7 is
| X | 5 | 11 | 9 |
| Y | -2 | 4 | 2 |
Now plot the points on a graph and we get the following required graph:
The point at which the paths of the submarine and the destroyer intersect are (5, -2)
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संबंधित प्रश्न
The sides of a triangle are given by the equations y - 2 = 0; y + 1 = 3 (x - 2) and x + 2y = 0.
Find, graphically :
(i) the area of a triangle;
(ii) the coordinates of the vertices of the triangle.
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 the following equations graphically :
x + 3y = 8
3x = 2 + 2y
Solve the following equations graphically :
2x - y = 9
5x + 2y = 27
Solve the following equations graphically :
x = 4
`(3x)/(3) - y = 5`
Solve the following equations graphically :
x - 2y = 2
`x/(2) - y` = 1
Find graphically the vertices of the triangle, whose sides are given by 3y = x + 18, x + 7y = 22 and y + 3x = 26.
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 = 7, x – y = 3
Solve graphically
y = 2x + 1, y + 3x – 6 = 0
