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Chapter 5: Q. 328 (page 678)

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

Part (a) (6,2)is a solution to the system.

Part (b)(9,-1)is not a solution to the system.

Step by step solution

01

Part (a) Step 1. Given Information

  • The given system is x+y=8y=x-4.
  • The point to be checked is(6,2).
02

Part (a) Step 2. Substitution 

  • Substitute (6,2)into the first equation and check if it satisfies the equation.

6+2=?88=8

  • Substitute the same point into the second equation and check if it satisfies the second equation.

role="math" localid="1648181369167" 2=?6-42=2

  • As both the equations are satisfied, the point (6,2)is a solution to the system.
03

Part (b) Step 1. Given Information

  • The given system is x+y=8y=x-4.
  • The point to be checked is(9,-1).
04

Part (b) Step 2. Substitution 

  • Substitute (9,-1)into the first equation and check if it satisfies the equation.

9-1=?88=8

  • Substitute the same point into the second equation and check if it satisfies the second equation.

-1=?9-4-1鈮�5

  • As the second equation is not satisfied, (9,-1)is not a solution of the system.

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