which ordered pair is in the solution set of the system of linear inequalities?\n$y>\\frac{3}{2}x…

which ordered pair is in the solution set of the system of linear inequalities?\n$y>\\frac{3}{2}x - 1$\n$y<\\frac{3}{2}x - 1$\n$(-5,2)$\n$(2,2)$\n$(5,2)$\nno solution

which ordered pair is in the solution set of the system of linear inequalities?\n$y>\\frac{3}{2}x - 1$\n$y<\\frac{3}{2}x - 1$\n$(-5,2)$\n$(2,2)$\n$(5,2)$\nno solution

Answer

Explanation:

Step1: Analyze the inequalities

We have (y>\frac{3}{2}x - 1) and (y<\frac{3}{2}x - 1). A point ((x,y)) must satisfy both inequalities simultaneously.

Step2: Check each ordered pair

  • For ((-5,2)):
    • Substitute into (y>\frac{3}{2}x - 1): (2>\frac{3}{2}\times(-5)-1=\frac{-15 - 2}{2}=-\frac{17}{2}) (True)
    • Substitute into (y<\frac{3}{2}x - 1): (2<\frac{3}{2}\times(-5)-1=-\frac{17}{2}) (False)
  • For ((2,2)):
    • Substitute into (y>\frac{3}{2}x - 1): (2>\frac{3}{2}\times2 - 1=3 - 1 = 2) (False, since (2\not>2))
  • For ((5,2)):
    • Substitute into (y>\frac{3}{2}x - 1): (2>\frac{3}{2}\times5 - 1=\frac{15 - 2}{2}=\frac{13}{2}) (False)

Answer:

no solution