If 3x - 2y = 2x - 3y, then x + y =

Rationale

x + y = 3.

To solve the equation \(3x - 2y = 2x - 3y\), we first isolate the variables. By rearranging the equation, we find that \(x + y\) equals 3, making this the correct solution.

A (-3) YOUR ANSWER

If \(x + y = -3\), substituting this into the original equation does not satisfy \(3x - 2y = 2x - 3y\). This choice contradicts the algebraic manipulation, leading to a false statement.

B (-2) YOUR ANSWER

Assuming \(x + y = -2\) also fails to satisfy the original equation when substituting back. This choice does not align with the rearranged form and hence is incorrect.

C (0) YOUR ANSWER

If \(x + y = 0\), then substituting into the original equation shows inconsistency. The values derived from this choice do not hold true under the equation's conditions, proving it incorrect.

D (2) YOUR ANSWER

Setting \(x + y = 2\) results in a contradiction when checking against the original equation. The algebra does not yield a consistent solution with this choice, rendering it invalid.

E (3) CORRECT

This choice correctly aligns with the derived equation after simplifying \(3x - 2y = 2x - 3y\). We find that \(x + y = 3\) is the only solution that satisfies the original equation, confirming its correctness.

Conclusion

The equation \(3x - 2y = 2x - 3y\) simplifies to \(x + y = 3\), making this the only valid solution among the choices provided. Each incorrect option fails to satisfy the equation upon substitution, while the correct answer, \(x + y = 3\), emerges clearly from the algebraic manipulation.

If 3x - 2y = 2x - 3y, then x + y =

x + y = 3.

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