Graphical Solution of a Pair of Linear Equations

Video Explanation

Question

Solve the following system of equations graphically:

\[ x – 2y = 6 \]

\[ 3x – 6y = 0 \]

Solution

Step 1: Write Both Equations in Convenient Form

Equation (1):

\[ x – 2y = 6 \Rightarrow y = \frac{x – 6}{2} \]

Equation (2):

\[ 3x – 6y = 0 \Rightarrow x – 2y = 0 \Rightarrow y = \frac{x}{2} \]

Step 2: Prepare Table of Values

For Equation (1): \(x – 2y = 6\)

x	y
6	0
2	-2

For Equation (2): \(3x – 6y = 0\)

x	y
0	0
4	2

Step 3: Graphical Representation

Plot the following points on the same Cartesian plane:

• Line 1: (6, 0) and (2, −2)
• Line 2: (0, 0) and (4, 2)

Join each pair of points to obtain two straight lines.

Step 4: Interpretation

The two lines have the same slope but different intercepts. Hence, they are parallel and do not intersect.

Conclusion

Since the two lines do not intersect, the given system of equations has no solution.

Thus, the graphical solution shows that the pair of linear equations is inconsistent.