Question
Solve the following system of equations graphically:
2x - 3y = 1, 4x - 3y + 1 = 0
2x - 3y = 1, 4x - 3y + 1 = 0
✓
Answer
On the graph paper, draw a horizontal line X'OX and a vertical line YOY' as the x-axis and y-axis, respectively.Graph of 2x - 3y = 1:
2x - 3y = 1 ⇒ 3y = (2x - 1) $\therefore\text{y}=\frac{2\text{x}-1}{3}\ ...(\text{i})$ Putting x = -1, we get: ⇒ y = -1 Putting x = 2, we get: ⇒ y = 1 Putting x = 5, we get: ⇒ y = 3 Thus, we have the following table for the equation 2x - 3y = 1.
Now, plot the points A(-1, -1), B(2, 1) and C(5, 3) on the graph paper. Join AB and BC to get the graph line AC. Extend it on both the sides. Thus, the line AC is the graph of 2x - 3y = 1.Graph of 4x - 3y + 1 = 0:
4x - 3y + 1 = 0 ⇒ 3y = (4x + 1) $\therefore\text{y}=\frac{4\text{x}-1}{3}\ ...(\text{ii})$ Putting x = -1, we get: ⇒ y = -1 Putting x = 2, we get: ⇒ y = 3 Putting x = 5, we get: ⇒ y = 7 Thus, we have the following table for the equation 4x - 3y + 1 = 0.
Now, plots the points P(2, 3) and Q(5, 7). The point A(-1, -1) has already been plotted. Join PA and QP to get the graph line AQ. Extend it on both the sides. Thus, the line AQ is the graph of the equation 4x - 3y + 1 = 0.
The two lines intersect at A(-1, -1). Thus, x = -1 and y = -1 is the solution of the given system of equations.
2x - 3y = 1 ⇒ 3y = (2x - 1) $\therefore\text{y}=\frac{2\text{x}-1}{3}\ ...(\text{i})$ Putting x = -1, we get: ⇒ y = -1 Putting x = 2, we get: ⇒ y = 1 Putting x = 5, we get: ⇒ y = 3 Thus, we have the following table for the equation 2x - 3y = 1.
|
x:
|
-1
|
2
|
5
|
|
y:
|
-1
|
1
|
3
|
4x - 3y + 1 = 0 ⇒ 3y = (4x + 1) $\therefore\text{y}=\frac{4\text{x}-1}{3}\ ...(\text{ii})$ Putting x = -1, we get: ⇒ y = -1 Putting x = 2, we get: ⇒ y = 3 Putting x = 5, we get: ⇒ y = 7 Thus, we have the following table for the equation 4x - 3y + 1 = 0.
|
x:
|
-1
|
2
|
5
|
|
y:
|
-1
|
3 | 7 |
The two lines intersect at A(-1, -1). Thus, x = -1 and y = -1 is the solution of the given system of equations.
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