The problem is asking whether the two systems of equations, labeled (A) and (B), are equivalent.

System (A):

1. $3x - 2y = 0$
2. $x + y = 5$

System (B):

1. $3x - 2y = 0$

To check if these systems are equivalent, we need to analyze the number of equations and their consistency.

• System (A) has two equations: one linear equation $3x - 2y = 0$, and another linear equation $x + y = 5$.
• System (B) only has one equation: $3x - 2y = 0$.

Clearly, these two systems are not equivalent. System (A) provides two conditions (two constraints), whereas System (B) provides only one condition. Thus, System (A) is more restrictive and likely has a different solution set compared to System (B).

Conclusion: The two systems are not equivalent, so the correct answer is False.

Do you need more details or have any questions?

Here are 5 related questions for further exploration:

1. What does it mean for two systems of equations to be equivalent?
2. How can we solve the system of equations in (A)?
3. What is the solution to $3x - 2y = 0$ alone in system (B)?
4. Can a system with fewer equations have the same solution as a system with more equations?
5. How do we graphically represent the solutions to both systems?

Tip: A system of equations is only considered equivalent if both systems yield exactly the same set of solutions for all variables.