Question
Solve the following system of equations graphically:
x + 2y + 2 = 0,
3x + 2y - 2 = 0
x + 2y + 2 = 0,
3x + 2y - 2 = 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 x + 2y + 2 = 0 and 3x + 2y - 2 = 0 Graph of x + 2y + 2 = 0: x + 2y + 2 = 0 $\Rightarrow\text{y}=\frac{-\text{x}-2}{2}\ \dots(1)$ Thus, we have the following table for x + 2y + 2 = 0
On the graph paper plot the points A(-2, 0), B(0, -1) and C(2, -2). Join AB and BC to get the graph line AC. Thus, the line AC is the graph of the equation of x + 2y + 2 = 0. Graph of 3x + 2y - 2 = 0: For graph of 3x + 2y - 2 = 0 $\Rightarrow\text{y}=\frac{-\text{3x}+2}{2}\ \dots(2)$ Thus, we have the following table for 3x + 2y - 2 = 0
Now, on the same graph paper plot the points P(0, 1) and Q(4, -5). The third point C(2, -2) has already been plotted. Join PC and QC to get the line PQ. Thus, line PQ is the graph of the equation 3x + 2y - 2 = 0.
The two graph lines intersect at C(2, -2). $\therefore$ x = 2, y = -2 is the solution of the given system of equations.
|
x:
|
-2 |
0
|
2
|
|
y:
|
0
|
-1
|
-2
|
|
x:
|
0
|
2
|
4
|
|
y:
|
1
|
-2
|
-5
|
The two graph lines intersect at C(2, -2). $\therefore$ x = 2, y = -2 is the solution of the given system of equations.
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