If the system of equations 2x + 3y = 6 and 4x + 6y = 12 is given, what can be in

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Question: If the system of equations 2x + 3y = 6 and 4x + 6y = 12 is given, what can be inferred about the lines represented by these equations?

Options:

Correct Answer: They are the same line.

Solution:

The second equation is a multiple of the first, indicating that both equations represent the same line.

If the system of equations 2x + 3y = 6 and 4x + 6y = 12 is given, what can be inferred about the lines represented by these equations?

If the system of equations 2x + 3y = 6 and 4x + 6y = 12 is given, what can be inferred about the lines represented by these equations?

Step 1: Look at the first equation: 2x + 3y = 6.
Step 2: Look at the second equation: 4x + 6y = 12.
Step 3: Notice that if you multiply the first equation by 2, you get: 2 * (2x + 3y) = 2 * 6, which simplifies to 4x + 6y = 12.
Step 4: Since the second equation is exactly the same as the result from Step 3, it means both equations represent the same line.
Step 5: Therefore, the lines represented by these equations are not different; they are the same line.

Linear Equations – Understanding the relationship between linear equations and their graphical representations.
Dependent and Independent Systems – Identifying whether a system of equations is dependent (same line) or independent (intersecting lines).