Question
Solve the following system of equations graphically:
3x + 2y = 4,
2x - 3y = 7
3x + 2y = 4,
2x - 3y = 7
✓
Answer
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 3x + 2y = 4: 3x + 2y = 4 $\Rightarrow\text{y}=\frac{4-\text{3x}}{2}$ Thus we have the following table for 3x + 2y = 4
Plot the points A(0, 2), B(2, -1) and C(-2, 5) 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 3x + 2y = 4. Graph of 2x - 3y = 7: $\Rightarrow\text{y}=\frac{\text{2x}-7}{3}$ Thus, we have the following table for 2x - 3y = 7 is
Now, on the same graph paper plot the points P(-1, -3) and Q(5, 1). The point B(2, -1) has already been plotted. Join PB and QB and extend it on both ways. Thus, line PQ is the graph of 2x - 3y = 7.
The two graph lines intersect at B(2, -1). $\therefore$ x = 2, y = -1 is the solution of the given system of equations.
|
x:
|
0 |
2
|
-2
|
|
y:
|
2
|
-1
|
5
|
|
x:
|
2
|
-1
|
5
|
|
y:
|
-1
|
-3
|
1
|
The two graph lines intersect at B(2, -1). $\therefore$ x = 2, y = -1 is the solution of the given system of equations.
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