Solve.
-The sum of three numbers is -6. The first, minus the second, plus 2 times the third, is -2. The third, plus 5 times the first, plus the second, is 2. What are the numbers?
A)2, -4, -4
B)2, 2, -4
C)No solution
D)-2, 4, 4

Question

Quizplus · Accepted Answer

Let the three numbers be a, b, and c. Then we have:

a + b + c = -6     ...... (1) 
a - b + 2c = -2    ...... (2) 
5a + b + c = 2     ...... (3)

Adding equation (2) to equation (3) yields:

6a + 3c = 0
=> 2a + c = 0
=> c = -2a

Substituting c = -2a into equation (1) yields:

a + b - 2a = -6
=> b - a = -6
=> b = a - 6

Substituting c = -2a and b = a - 6 into equation (2) yields:

a - (a - 6) + 2(-2a) = -2
=> -3a - 6 = -2
=> a = 4

Substituting a = 4 into c = -2a yields:

c = -2(4) = -8

Substituting a = 4 and c = -8 into equation (1) yields:

4 + b - 8 = -6
=> b = -2

Therefore, the three numbers are 4, -2, and -8, which corresponds to answer choice A.

Solve. -The Sum of Three Numbers Is -6. the First, Minus