Solve the system of inequalities: {4-(y-1)/3≥y (7y-1)/8≥6

Solve the system of inequalities:

• \(4-\frac{y-1}{3} \ge y\)
• \(\frac{7y-1}{8} \ge 6\)

Пошаговое решение:

1. Solve the first inequality:

   • \(4 - \frac{y-1}{3} \ge y\)
   • Multiply both sides by 3:
   • \(3(4 - \frac{y-1}{3}) \ge 3y\)
   • \(12 - (y-1) \ge 3y\)
   • \(12 - y + 1 \ge 3y\)
   • \(13 - y \ge 3y\)
   • \(13 \ge 4y\)
   • \(y \le \frac{13}{4}\)

2. Solve the second inequality:

   • \(\frac{7y-1}{8} \ge 6\)
   • Multiply both sides by 8:
   • \(7y - 1 \ge 48\)
   • \(7y \ge 49\)
   • \(y \ge 7\)

3. Find the intersection of the solutions:

   • We have \(y \le \frac{13}{4}\) and \(y \ge 7\).
   • Since \(\frac{13}{4} = 3.25\), we have \(y \le 3.25\) and \(y \ge 7\).
   • There is no intersection between these two intervals, so there is no solution.

Answer: There is no solution for this system of inequalities.