1. **State the problem:** We have the system of equations: $$2x - 3y = 4$$ $$-7x + 2y = 3$$ We need to check if each ordered pair $(x,y)$ is a solution to this system. 2. **Recall the rule:** A pair $(x,y)$ is a solution if it satisfies both equations simultaneously. 3. **Check each pair:** - For $(0,5)$: - First equation: $2(0) - 3(5) = 0 - 15 = -15 \neq 4$ - So, $(0,5)$ is **not** a solution. - For $(-3,-9)$: - First equation: $2(-3) - 3(-9) = -6 + 27 = 21 \neq 4$ - So, $(-3,-9)$ is **not** a solution. - For $(8,4)$: - First equation: $2(8) - 3(4) = 16 - 12 = 4$ (satisfies first) - Second equation: $-7(8) + 2(4) = -56 + 8 = -48 \neq 3$ - So, $(8,4)$ is **not** a solution. - For $(-2,-1)$: - First equation: $2(-2) - 3(-1) = -4 + 3 = -1 \neq 4$ - So, $(-2,-1)$ is **not** a solution. 4. **Conclusion:** None of the given pairs satisfy both equations, so none are solutions to the system. **Final answer:** - (0,5): No - (-3,-9): No - (8,4): No - (-2,-1): No