Graphical Solution of a Pair of Linear Equations
Video Explanation
Question
Solve the following system of equations graphically:
\[ 2x + 3y + 5 = 0 \]
\[ 3x – 2y – 12 = 0 \]
Solution
Step 1: Write Both Equations in Convenient Form
Equation (1):
\[ 2x + 3y + 5 = 0 \Rightarrow 3y = -2x – 5 \Rightarrow y = \frac{-2x – 5}{3} \]
Equation (2):
\[ 3x – 2y – 12 = 0 \Rightarrow -2y = -3x + 12 \Rightarrow y = \frac{3x – 12}{2} \]
Step 2: Prepare Table of Values
For Equation (1): \(2x + 3y + 5 = 0\)
| x | y |
|---|---|
| -1 | -1 |
| 2 | -3 |
For Equation (2): \(3x – 2y – 12 = 0\)
| x | y |
|---|---|
| 4 | 0 |
| 2 | -3 |
Step 3: Graphical Representation
Plot the following points on the same Cartesian plane:
- Line 1: (−1, −1) and (2, −3)
- Line 2: (4, 0) and (2, −3)
Join each pair of points to obtain two straight lines.
The two lines intersect at the point:
\[ (2,\, -3) \]
Conclusion
The graphical solution of the given system of equations is:
\[ \boxed{x = 2,\; y = -3} \]
Hence, the two lines intersect at the point (2, −3).