Question

1. which ordered pairs are solutions to this system? circle all that apply. (5,0) (0,0) (-2,0) (2,4) (4,-1) 23. which linear inequalities match the system to the right? a. y > -3x + 5 & y ≤ x - 2 b. y > -3x + 5 & y < x - 2 c. y > 3x + 5 & y ≤ -x - 2 d. y ≥ -3x + 5 & y ≤ x - 2

Explanation:

Step1: Recall the test - point method for inequalities

For an ordered pair \((x,y)\), substitute \(x\) and \(y\) values into the inequalities of the system.

Step2: Consider the system of inequalities \(y > - 3x+5\) and \(y\leq x - 2\)

Test \((5,0)\):

For \(y > - 3x + 5\), substitute \(x = 5\) and \(y = 0\): \(0>-3\times5 + 5=0>-15 + 5=0>-10\) (True).
For \(y\leq x - 2\), substitute \(x = 5\) and \(y = 0\): \(0\leq5 - 2=0\leq3\) (True).

Test \((4,-1)\):

For \(y > - 3x + 5\), substitute \(x = 4\) and \(y=-1\): \(-1>-3\times4 + 5=-1>-12 + 5=-1>-7\) (True).
For \(y\leq x - 2\), substitute \(x = 4\) and \(y=-1\): \(-1\leq4 - 2=-1\leq2\) (True).

Test \((0,0)\):

For \(y > - 3x + 5\), substitute \(x = 0\) and \(y = 0\): \(0>-3\times0+5=0 > 5\) (False).

Test \((2,4)\):

For \(y > - 3x + 5\), substitute \(x = 2\) and \(y = 4\): \(4>-3\times2 + 5=4>-6 + 5=4>-1\) (True).
For \(y\leq x - 2\), substitute \(x = 2\) and \(y = 4\): \(4\leq2 - 2=4\leq0\) (False).

Test \((-2,0)\):

For \(y > - 3x + 5\), substitute \(x=-2\) and \(y = 0\): \(0>-3\times(-2)+5=0>6 + 5=0>11\) (False).

Step3: Determine the solutions

The ordered - pairs \((5,0)\) and \((4,-1)\) satisfy both inequalities in the system \(y > - 3x + 5\) and \(y\leq x - 2\).

For question 23, the system of inequalities \(y > - 3x + 5\) and \(y\leq x - 2\) corresponds to option B.

Answer:

1. Circle \((5,0)\), \((4,-1)\)
2. B. \(y > - 3x + 5\) & \(y\leq x - 2\)