Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
x + 2y = 4
⇒ x = 4 - 2y
The table of x + 2y = 4 is
| X | 2 | - 4 | 12 |
| Y | 1 | 4 | - 4 |
3x - 2y = 4
⇒ x = `(4 + 2y)/(3)`
The table of 3x - 2y = 4 is
| X | 2 | 4 | 6 |
| Y | 1 | 4 | 7 |
Now plotting the points on a graph and we get the following required graph:
Therefore the solution of the given system of equations is (2,1).
Thus the vertices of the triangle are:
A(2,1), B`(4/3,0)`and C(4,0)
AB ⊥ BC and D ≡ (2,0)
AD = 1 and BC = `2(2)/(3) "units" = (8)/(3) "units"`
Area of the triangle ABC = `(1)/(2) xx "AD" xx "BC"`
= `(1)/(2) xx 1 xx (8)/(3)`
= `(4)/(3)"sq.units"`
= `1(1)/(3)"sq.units"`
APPEARS IN
संबंधित प्रश्न
Solve graphically the simultaneous equations given below. Take the scale as 2 cm = 1 unit on both the axes.
x - 2y - 4 = 0
2x + y = 3
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.
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 + 4y + 9 = 0
3y = 5x - 1
Solve the following equations graphically :
`2 + (3y)/x = (6)/x`
`(6x)/y - 5 = (4)/y`
Find graphically the vertices of the triangle, whose sides are given by 3y = x + 18, x + 7y = 22 and y + 3x = 26.
Solve graphically
x = −3, y = 3
Two cars are 100 miles apart. If they drive towards each other they will meet in 1 hour. If they drive in the same direction they will meet in 2 hours. Find their speed by using graphical method.
