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:
\[ 2x – 3y = 6 \]
\[ x + y = 1 \]
Solution
Step 1: Write Both Equations in Convenient Form
Equation (1):
\[ 2x – 3y = 6 \Rightarrow 3y = 2x – 6 \Rightarrow y = \frac{2}{3}x – 2 \]
Equation (2):
\[ x + y = 1 \Rightarrow y = 1 – x \]
Step 2: Prepare Tables of Values
For Equation (1): \(2x – 3y = 6\)
| x | y |
|---|---|
| 0 | -2 |
| 3 | 0 |
For Equation (2): \(x + y = 1\)
| x | y |
|---|---|
| 0 | 1 |
| 1 | 0 |
Step 3: Graphical Representation
Plot the following points on the same Cartesian plane:
- Line 1: (0, −2) and (3, 0)
- Line 2: (0, 1) and (1, 0)
Join each pair of points to obtain two straight lines.
The two straight lines intersect at exactly one point.
Conclusion
Since the two lines intersect at a single point, the given system of linear equations has a unique solution.
Hence, the system of equations is consistent.