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Chapter 5: Q. 5.101 (page 662)

Determine whether the ordered pair is a solution to the system.

x-5y>102x+3y>-2

a) (3,-1)

b)(6,-3)

Short Answer

Expert verified

Part (a) The ordered pair is not a solution to the set.

Part (b) The ordered pair is a solution to the set.

Step by step solution

01

Part (a) Step 1. Given information

The given system is x-5y>102x+3y>-2and the ordered pair is (3,-1).

02

Part (a) Step 2. Substitute the values into the inequalities

  • Substitute x=3,y=-1into the first given inequality.

role="math" localid="1647846938951" 3-5(-1)>?103+5>?108>10False

  • Substitute x=3,y=-1into the second inequality.

2(3)+3(-1)>?-26-3>?-23>-2True

  • Since first inequality is not satisfied, the given ordered pair is not a solution to the system.
03

Part (b). Step 1. Given Information

The given system is x-5y>102x+3y>-2and the ordered pair is(6,-3).

04

Part  (b). Step 2. Substitute the values into the inequalities

  • Substitute x=6,y=-3into the first given inequality.

6-5(-3)>?106+15>?1021>10True

  • Substitute x=6,y=-3into the second given inequality.

2(6)+3(-3)>?-212-9>?-23>-2True

  • Since both of the inequalities are satisfied, the ordered pair is a solution to the set.

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