Is This Correct?

Question

Solve:

2x −3y +z = 17

x −z +4y = −2

y + 5z − 2x = 85

Then evaluate: xyz =

(A) -54

(B) (2+4/5)

(C) 216

(D) ∅

(E) None of the above

For this I got; (C) 216. Is this correct?

Answer 1

Do you want to know just (1) that the answer is correct or (2) that the process that you followed is correct?

One of the most serious problems in our education system is the emphasis on getting the "right answer" whether or not you understand how to get an answer. Thus, when the problem is slightly changed for the test, students no longer know how to solve it (since they simply memorized the answers).

If you learn how to perform elimination to solve this system of equations, then you will find matrix operations to be much easier when you study them in later math courses.

First, put the variables in x, y, z order:

2x − 3y + z = 17 {eq1}

x + 4y − z = −2 (eq2)

-2x + y + 5z = 85 (eq3)

Now, add eq1 to eq2, then add 5*eq2 to eq3, to get:

3x + y = 15 [eq4]

3x + 21y = 75 [eq5]

-------------------------------- [elimination, subtract eq4 from eq5]

20y = 60

y = 3

3x + 3 = 15 [eq4 again]

x = 4

Now, use any of the 3 equations to find z:

2(4) - 3(3) + z = 17

z = 18

(3)(4)(18) = 216 [You not only got the right answer, you probably did correctly.]

At this point, putting the values for x, y, and z into the three equations is a smart way of checking your work.

However, on a timed multiple-choice test, it is sometimes faster to plug in the possible answers (called the distractors) than it is to "solve" the problem the usual way.

Answer 2

It shouldn't be hard for you to check for yourself whether your answer is correct or not. Just check that the values you obtained for x, y and z satisfy the 3 equations, and then calculate their product.