1. **State the problem:** Determine which pair of equations could not be used to solve the system: $$4x + 2y = 22$$ $$-2x + 2y = -8$$ 2. **Recall the rule:** Equivalent systems can be formed by multiplying or adding equations but must represent the same solution set. 3. **Check each option:** - (1) $$4x + 2y = 22$$ and $$2x - 2y = 8$$ Multiply second by 2: $$4x - 4y = 16$$, which differs from original second equation, so not equivalent. - (2) $$4x + 2y = 22$$ and $$-4x + 4y = -16$$ Multiply original second by 2: $$-4x + 4y = -16$$, matches option (2), so equivalent. - (3) $$12x + 6y = 66$$ and $$6x - 6y = 24$$ Multiply original first by 3: $$12x + 6y = 66$$, second by 3: $$-6x + 6y = -24$$, but option has $$6x - 6y = 24$$ which is not equivalent. - (4) $$8x + 4y = 44$$ and $$-8x + 8y = -8$$ Multiply original first by 2: $$8x + 4y = 44$$, second by 4: $$-8x + 8y = -32$$, option has $$-8x + 8y = -8$$, not equivalent. 4. **Conclusion:** Option (1) is not equivalent because the second equation is not a multiple or combination of the original second equation. **Final answer:** (1) 4x + 2y = 22 and 2x - 2y = 8