Question
Solve each of the following systems of equations graphically:
2x + 3y = 2
x – 2y = 8
Solution:
On a graph paper, draw a horizontal line X’OX and a vertical line YOY’ representing the x-axis and y-axis, respectively.
Graph of 2x + 3y = 2
2x + 3y = 2
=> 3y = (2 – 2x)
=> 3y = 2(1 – x)
=> y= 2(1 – x) / 3 …..(i)
Putting x = 1, we get y = 0
Putting x = -2, we get y = 2
Putting x = 4, we get y = -2
Thus, we have the following table for the equation 2x + 3y = 2
| x | 1 | -2 | 4 |
| y | 0 | 2 | -2 |
Now, plot the points A(1, 0), B(-2, 2) and C(4, -2) on the graph paper. Join AB and AC to get the graph line BC. Extend it on both ways. Thus, the line BC is the graph of 2x + 3y = 2.
Graph of x – 2y = 8
x – 2y = 8
=> 2y = x – 8
=> y = (x – 8)/2 …..(ii)
Putting x = 2, we get y = -3
Putting x = 4, we get y = -2
Putting x = 0, we get y = -4
Thus, we have the following table for the equation x – 2y = 8
| x | 2 | 4 | 0 |
| y | -3 | -2 | -4 |
Now, plot the points P(0, -4) and Q(2, -3). The point C(4, -2) has already been plotted. Join PQ and QC and extend it on both ways. Thus, line PC is the graph of x – 2y = 8.
The two graph lines intersect at C(4, -2).
∴ x = 4 and y = -2 are the solutions of the given system of equations.
