Question
Solve the following system of equations graphically:
2x + 3y = 8,
x - 2y + 3 = 0
2x + 3y = 8,
x - 2y + 3 = 0
✓
Answer
On a graph paper, draw a horizontal line X'OX and a vertical line YOY' representing the x-axis and y-axis, respectively. Given equations are 2x + 3y = 8 and x - 2y + 3 = 0 Graph of 2x + 3y = 8: 2x + 3y = 8 $\Rightarrow\text{y}=\frac{8-\text{2x}}{3}\ \dots(1)$ Thus we have the following table for 2x + 3y = 8
On the graph paper plot the points A(1, 2), B(-5, 6) and C(7, -2). Join AB and AC to get the graph line BC. Thus, the line AC is the equation of 2x + 3y = 8. Graph of x - 2y + 3 = 0: For graph of x - 2y + 3 = 0 $\Rightarrow\text{y}=\frac{\text{x}+3}{2}\ \dots(2)$ Thus, we have the following table for x - 2y + 3 = 0
Now, on the same graph paper plot the points P(3, 3) and Q(-3, 0). The point A(1, 2) has already been plotted. Join PA and QA to get the line PQ. Thus, line PQ is the graph of the equation x - 2y + 3 = 0.
The two graph lines intersect at A(1, 2). $\therefore$ x = 1, y = -2 is the solution of the given system of equations.
|
x:
|
1 |
-5
|
7
|
|
y:
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2
|
6
|
-2
|
|
x:
|
1
|
3
|
-3
|
|
y:
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2
|
3
|
0
|
The two graph lines intersect at A(1, 2). $\therefore$ x = 1, y = -2 is the solution of the given system of equations.
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→|
Class
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0-20
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20-40
|
40-60
|
60-80
|
80-100
|
100-120
|
|
Frequency
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5
|
$f_1$
|
10
|
$f_2$
|
7
|
8
|