Advertisements
Advertisements
प्रश्न
Solve the following equations graphically :
x + 3y = 8
3x = 2 + 2y
उत्तर
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.
APPEARS IN
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.
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.
Use the graphical method to find the value of 'x' for which the expressions `(3x + 2)/(2) and (3)/(4)x - 2`
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?
Solve the following equations graphically :
2x - y = 9
5x + 2y = 27
Solve the following equations graphically :
x + 4y + 9 = 0
3y = 5x - 1
Solve the following system of linear equations graphically :
4x - 5y - 20 = 0
3x + 3y - 15 = 0
Determine the vertices of the triangle formed by the lines, represented by the above equations and the y-axis.
Solve the following system of equations graphically:
2x = 23 - 3y
5x = 20 + 8y
Also, find the area of the triangle formed by these lines and x-axis in each graph.
Solve graphically
x + y = 7, x – y = 3
Solve graphically
`x/2 + y/4` = 1, `x/2 + y/4` = 2
