Question

Nswer two questions about Systems A AA and B BB: System A AA start text, end text System B BB { − 3 x + 12 y = 15 7 x − 10 y = − 2 ⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ ​ −3x+12y=15 7x−10y=−2 ​ { − x + 4 y = 5 7 x − 10 y = − 2 ⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ ​ −x+4y=5 7x−10y=−2 ​ 1) How can we get System B BB from System A AA? Choose 1 answer: Choose 1 answer: (Choice A) A Replace one equation with the sum/difference of both equations (Choice B) B Replace only the left-hand side of one equation with the sum/difference of the left-hand sides of both equations (Choice C) C Replace one equation with a multiple of itself (Choice D) D Replace one equation with a multiple of the other equation

Answer 1

Answer:

(Choice C) C Replace one equation with a multiple of itself

Step-by-step explanation:

Since system A has the equations

-3x + 12y = 15 and 7x - 10y = -2 and,

system B has the equations

-x + 4y = 5 and 7x - 10 y = -2.

To get system B from system A, we notice that equation -x + 4y = 5 is a multiple of -3x + 12y = 15 ⇒ 3(-x + 4y = 5) = (-3x + 12y = 15).

So, (-x + 4y = 5) = (1/3) × (-3x + 12y = 15)

So, we replace the first equation in system B by 1/3 the first equation in system A to obtain the first equation in system B.

So, choice C is the answer.

We replace one equation with a multiple of itself.