Answer:
(d) 3 × [A2] + [A1] ⇒ [B1]
(c) -2 × [B1] + [B2] ⇒ [C2]
Explanation:
Given three systems of equations, you want to know the operations that transform one system to the next.
A to B
Equation B2 is unchanged from equation A2, eliminating choices B and C.
Equation B1 is not a simple multiple of equation A1, eliminating choice A.
Knowing the answer is choice D, we need to find the multiplier k of equation A2 that is being added to A1. We can find that using the x-coefficients:
k(-3) +5 = -4
-3k = -9 . . . . . subtract 5
k = 3 . . . . . . . divide by -3
Then we have ...
3 × [A2] + [A1] ⇒ [B1] . . . . . . . choice D
B to C
Using the same tactics as above, we see that [C1] is unchanged from [B1], eliminating choices A and D.
[C2] is not a simple multiple of [B2], eliminating choice B.
Using the y-coefficient to find k, we have ...
k(1) +2 = 0
k = -2 . . . . . . . . subtract 2
Then we have ...
-2 × [B1] + [B2] ⇒ [C2] . . . . . . . . choice C
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Additional comment
We found the equation multiplier, which we called "k", by looking at an arbitrary variable coefficient. Which of the numbers we use in this process is immaterial. That is, we could use either coefficient, or the right-side constant, and we would get the same result.
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