Graphical Solution of a Pair of Linear Equations
Video Explanation
Question
Solve the following system of equations graphically:
\[ 3x + y + 1 = 0 \]
\[ 2x – 3y + 8 = 0 \]
Solution
Step 1: Write Both Equations in the Form \(y = mx + c\)
Equation (1):
\[ 3x + y + 1 = 0 \Rightarrow y = -3x – 1 \]
Equation (2):
\[ 2x – 3y + 8 = 0 \Rightarrow -3y = -2x – 8 \Rightarrow y = \frac{2x + 8}{3} \]
Step 2: Prepare Table of Values
For Equation (1): \(3x + y + 1 = 0\)
| x | y |
|---|---|
| 0 | -1 |
| -1 | 2 |
For Equation (2): \(2x – 3y + 8 = 0\)
| x | y |
|---|---|
| -1 | 2 |
| 1 | \(\frac{10}{3}\) |
Step 3: Graphical Representation
Plot the following points on the same Cartesian plane:
- Line 1: (0, −1) and (−1, 2)
- Line 2: (−1, 2) and (1, 10/3)
Join each pair of points to obtain two straight lines.
The two lines intersect at the point:
\[ (-1,\,2) \]
Conclusion
The graphical solution of the given system of equations is:
\[ \boxed{x = -1,\; y = 2} \]
Hence, the two lines intersect at the point \((-1, 2)\).