Advertisements
Advertisements
Question
Solve the following equations graphically :
x + 3y = 8
3x = 2 + 2y
Advertisements
Solution
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
RELATED QUESTIONS
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).
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.
Use the graphical method to find the value of 'x' for which the expressions `(3x + 2)/(2) and (3)/(4)x - 2`
Solve the following equations graphically :
x = 4
`(3x)/(3) - y = 5`
Solve the following equations graphically :
3y = 5 - x
2x = y + 3
Solve the following equations graphically :
x+ 2y - 7 = 0
2x - y - 4 = 0
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.
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/2 + y/4` = 1, `x/2 + y/4` = 2
Solve graphically
x – y = 0, y + 3 = 0
