Answer:
(a) 2 × [A1] + [A2] → [B2] . . . choice C
(b) 4 × [B2] + [B1] → [C1] . . . choice D
Step-by-step explanation:
You want to identify the transformations of the given systems of equations that result in the elimination of the y-variable.
(a) A to B
You observe that equation [A1] matches equation [B1], so there has been no change that gives a new [B1]. (This eliminates choices A and D.)
The change that gets from [A2] to [B2] is that the x-coefficient has been increased by 14 from -11 to +3. That value (14) is 2 times the x-coefficient in [A1].
As a check, we notice the y-coefficient is decreased from 9 in [A2] to 1 in [B2]. That change (-8) is 2 times the y-coefficient in [A1]. Taken together, these observations tell you that ...
2 × Equation [A1] + Equation [A2] → Equation [B2] . . . . . . choice C
(b) B to C
You observe that equation [B2] matches equation [C2], so there has been no change that gives a new [C2]. (This eliminates choices B and C.)
The change that gets from [B1] to [C1] is that the y-coefficient has been increased from -4 to 0. That change (4) is 4 times the y-coefficient in [B2].
You also notice that the x-coefficient has increased from 7 to 19, a change of +12 that is 4 times the x-coefficient in [B2]. These observations tell you that ...
4 × Equation [B2] + Equation [B1] → Equation [C1] . . . . . . choice D
