Graphical Solution of a Pair of Linear Equations
Video Explanation
Question
Determine, by drawing graphs, whether the following system of linear equations has a unique solution or not:
\[ 2y = 4x – 6 \]
\[ 2x = y + 3 \]
Solution
Step 1: Write Both Equations in Convenient Form
Equation (1):
\[ 2y = 4x – 6 \Rightarrow y = 2x – 3 \]
Equation (2):
\[ 2x = y + 3 \Rightarrow y = 2x – 3 \]
Step 2: Prepare Tables of Values
For Equation (1): \(y = 2x – 3\)
| x | y |
|---|---|
| 0 | -3 |
| 2 | 1 |
For Equation (2): \(y = 2x – 3\)
| x | y |
|---|---|
| 1 | -1 |
| 3 | 3 |
Step 3: Graphical Representation
Plot the following points on the same Cartesian plane:
- Line 1: (0, −3) and (2, 1)
- Line 2: (1, −1) and (3, 3)
Join each pair of points to obtain straight lines.
Both equations represent the same straight line; hence, the two lines coincide.
Conclusion
Since the two lines coincide, the given system of linear equations has infinitely many solutions.
Hence, the system of equations does not have a unique solution and is consistent (dependent).