Question: Which ordered pair is a solution of the equation?
3x + 3y = -x + 5y
Choose 1 answer:
A Only (1, 2)
B Only (2, 4)
C Both (1, 2) and (2, 4)
D Neither
1. **State the problem:** We need to determine which ordered pair(s) satisfy the equation $$3x + 3y = -x + 5y$$.
2. **Rewrite the equation:**
$$3x + 3y = -x + 5y$$
3. **Bring all terms to one side:**
$$3x + 3y + x - 5y = 0$$
4. **Combine like terms:**
$$3x + x + 3y - 5y = 0$$
$$4x - 2y = 0$$
5. **Simplify the equation:**
Divide both sides by 2:
$$\cancel{2} \times (2x - y) = \cancel{2} \times 0$$
$$2x - y = 0$$
6. **Rewrite the simplified equation:**
$$y = 2x$$
7. **Check each ordered pair:**
- For (1, 2):
$$y = 2$$ and $$2x = 2 \times 1 = 2$$
Since $$y = 2x$$ holds, (1, 2) is a solution.
- For (2, 4):
$$y = 4$$ and $$2x = 2 \times 2 = 4$$
Since $$y = 2x$$ holds, (2, 4) is also a solution.
8. **Conclusion:** Both ordered pairs satisfy the equation.
**Final answer:** C Both (1, 2) and (2, 4)