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Chapter 4: Q 329 (page 479)

In the following exercises, determine if the following points are solutions to the given system of

equations.

x+y=8y=x-4

(a) (6,2)

(b) (9.-1)

Short Answer

Expert verified

For (a), the ordered pair, (6,2)is a solution of the system of linear equations.

For (b), the ordered pair ,(9,-1) is not a solution of the system of linear equations.

Step by step solution

01

Step 1. Given information

The given linear equations

x+y=8y=x-4

(a) (6,2)

(b) (9.-1)

02

Checking the values   

Firstsubstitutex=6,y=2intotheequationx+y=8x+y=86+2=88=8Thisistrue.Alsosubstitutex=6,y=2intotheequationy=x-4y=x-42=6-42=2Thisistrue.Hnece,theorderedpair(6,2)isasolutionofthesystemoflinearequations.

03

Substitute for another equation 

Firstsubstitutex=9,y=-1intotheequationx+y=8x+y=89-1=88=8Thisistrue.Alsosubstitutex=9,y=-1Intotheequationy=x-4y=x-4-1=9-4-1=5Thisisnottrue.Therefore,theorderedpair(9,-1)isnotasolutionofthesystemoflinearequations.

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