Which of the following points shows a solution to the simultaneous inequalities: y > 1/2 x + 5 and y < -2x + 1

Answer 1

To determine which points are solutions to the simultaneous inequalities \( y > \frac{1}{2}x + 5 \) and \( y < -2x + 1 \), we need to check each point against both inequalities.

1. Point A: (x1, y1)

   • Check if \( y1 > \frac{1}{2}x1 + 5 \)
   • Check if \( y1 < -2x1 + 1 \)

2. Point B: (x2, y2)

   • Check if \( y2 > \frac{1}{2}x2 + 5 \)
   • Check if \( y2 < -2x2 + 1 \)

3. Point C: (x3, y3)

   • Check if \( y3 > \frac{1}{2}x3 + 5 \)
   • Check if \( y3 < -2x3 + 1 \)

4. Point D: (x4, y4)

   • Check if \( y4 > \frac{1}{2}x4 + 5 \)
   • Check if \( y4 < -2x4 + 1 \)

You must substitute the \( x \) and \( y \) coordinates of each point into both inequalities and see which point(s) satisfy both conditions.

If you provide specific points, I can help you evaluate them against the inequalities!