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Chapter 5: Q. 276 (page 672)

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

4x-y<10-2x+2y>-8a.(5,-2)b.(-1,3)

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 set is4x-y<10-2x+2y>-8and the ordered pair is(5,-2).

02

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

  • Substitute x=5,y=-2into the first given inequality.

4(5)-(-2)<?1020+2<?1022<10False

  • Substitute x=5,y=-2into the second inequality.

-2(5)+2(-2)>?-8-10-4>?-8-14>-8False

  • Since both of the inequalities are not satisfied, the given ordered pair is not a solution to the system.
03

Part b. Step 1, Given Information

The given set is 4x-y<10-2x+2y>-8and the ordered pair is (-1,3).

04

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

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

4(-1)-(3)<10?-4-3<10?-7<10True

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

-2(-1)+2(3)>?-82+6>?-88>-8true

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

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