Subjects algebra

Inequality Y Coordinates

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1. **State the problem:** We need to find the y-coordinates of all points that satisfy the system of inequalities: $$y > 2x - 1$$ $$2x > 5$$ 2. **Rewrite the second inequality:** $$2x > 5 \implies x > \frac{5}{2}$$ This means the solution region is to the right of the vertical line $x = \frac{5}{2}$. 3. **Analyze the first inequality:** $$y > 2x - 1$$ This means $y$ is above the line $y = 2x - 1$. 4. **Find the minimum y-value in the solution region:** Since $x > \frac{5}{2}$, the smallest $x$ in the solution region is just greater than $\frac{5}{2}$. Calculate $y$ at $x = \frac{5}{2}$: $$y > 2 \times \frac{5}{2} - 1 = 5 - 1 = 4$$ 5. **Interpretation:** For all $x > \frac{5}{2}$, $y$ must be greater than $2x - 1$, which is always greater than 4 because $2x - 1$ increases as $x$ increases. Therefore, the y-coordinates satisfying both inequalities must be greater than 4. **Final answer:** $$y > 4$$ This corresponds to option B.