Which of the following ordered triples is a solution of the system ?
A) (- 9, -5,-9)
B) (-9, 5, 28)
C) (- 9,-18,-9)
D) (- 9,-5, 9)

Question

Which of the following ordered triples is a solution of the system  ?
A) (- 9, -5,-9) 
B) (-9, 5, 28) 
C) (- 9,-18,-9) 
D) (- 9,-5, 9)

Quizplus · Accepted Answer

To check if an ordered triple is a solution of the system, we need to plug in the values of the variables and see if all three equations are true.

For choice A: 
3(-9) - 4(-5) = -27 + 20 = -7 (not equal to 14) 
-2(-9) + 7(-5) = 18 - 35 = -17 (not equal to -8) 
-5(-9) - 6(-5) = 45 + 30 = 75 (not equal to 108) 
Therefore, (-9, -5, -9) is not a solution.

For choice B: 
3(-9) - 4(5) = -27 - 20 = -47 (not equal to 14) 
-2(-9) + 7(5) = 18 + 35 = 53 (not equal to -8) 
-5(-9) - 6(5) = 45 - 30 = 15 (not equal to 108) 
Therefore, (-9, 5, 28) is not a solution.

For choice C: 
3(-9) - 4(-18) = -27 + 72 = 45 (not equal to 14) 
-2(-9) + 7(-18) = 18 - 126 = -108 (not equal to -8) 
-5(-9) - 6(-18) = 45 + 108 = 153 (not equal to 108) 
Therefore, (-9, -18, -9) is not a solution.

For choice D: 
3(-9) - 4(-5) = -27 + 20 = -7 (true) 
-2(-9) + 7(-5) = 18 - 35 = -17 (true) 
-5(-9) - 6(5) = 45 - 30 = 15 (true) 
Therefore, (-9, -5, 9) is a solution of the system.

Which of the Following Ordered Triples Is a Solution of the System