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Chapter 5: Q. 282 (page 672)

In the following exercises, determine whether each ordered pair is a solution to the system.

5x-3y<-210x+6y>4a.(15,23)b.(-310,76)

Short Answer

Expert verified

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

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

Step by step solution

01

Part a. Step 1. Given Information

The given set is 5x-3y<-210x+6y>4and the ordered pair is(15,23).

02

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

  • Substitute x=15,y=23into the first given inequality.

5(15)-3(23)<?-21-2<?-2-1<-2False

  • Substitute into the second inequality.

10(15)+6(23)>?42+4>?46>4True

  • Since both of the inequalities are satisfied, the given ordered pair is a solution to the system.
03

Part b. Step 1. Given information

The given set is 5x-3y<-210x+6y>4and the ordered pair is(-310,76).

04

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

  • Substitute x=-310,y=76into the first given inequality.

5(-310)+6(76)>?4-32+7>?4112>4True

  • Substitute x=-310,y=76into the second given inequality.

10(-310)+6(76)>?4-3+7>?44>4False

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

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