Question

What is the solution to the system of equations?

Answer 1

Answer:

  (b)  (-3, 2, -5)

Step-by-step explanation:

The solution to the system of equations will satisfy every equation. If it fails to satisfy any equation, it is not a solution.

Strategy

The system of equations does not seem to lend itself to simple solution by substitution or elimination. Hence, a reasonable strategy for finding the answer is to try the offered choices. Of course, a calculator can be used to find the answer almost as quickly.

Check

Using the third equation, we can check the answer choices fairly easily. That equation involves the least number of arithmetic operations. Substituting for (x, y, z), we have ...

  a) 3(1) -(11) -(5) = -13 ≠ -6

  b) 3(-3) -(2) -(-5) = -6 . . . . . . a potential solution

  c) 3(1) -(8) -(0) = -5 ≠ -6

  d) 3(-1) -(3) -(4) = -10 ≠ -6

The only viable choice is (-3, 2, -5).

Check

In the other two equations, we have for this solution, ...

  2(-3) -2(2) +(-5) = -15 . . . . works in the first equation

  6(-3) -3(2) -(-5) = -18 . . . . works in the second equation