Determine by Drawing Graphs Whether the System of Linear Equations Has a Unique Solution: 2y = 4x − 6, 2x = y + 3

Video Explanation

Watch the video below to understand the complete solution step by step:

Solution

Question:
Determine, by drawing graphs, whether the following system of linear equations has a unique solution or not:
2y = 4x − 6
2x = y + 3

Step 1: Rewrite the Equations in Slope-Intercept Form

For 2y = 4x − 6:

y = 2x − 3

For 2x = y + 3:

y = 2x − 3

Step 2: Compare the Two Equations

Slope of first line = 2
Slope of second line = 2

The y-intercepts of both lines are also the same:

y-intercept = −3

Step 3: Graphical Interpretation

Since both equations reduce to the same equation, their graphs coincide completely when drawn on the same Cartesian plane.

Therefore, every point on the line satisfies both equations.

Final Answer

∴ The given system of linear equations does not have a unique solution. It has infinitely many solutions.

Conclusion

Since the two equations represent the same straight line, the system of linear equations is consistent and dependent, and hence has infinitely many solutions.