contestada

Answer two questions about Systems AAA and BBB:
System AAA \text{\quad}start text, end text System BBB
\begin{cases}6x-5y=1\\\\-2x+2y=-1\end{cases}
⎩
⎪
⎪
⎨
⎪
⎪
⎧
​

6x−5y=1
−2x+2y=−1
​
\begin{cases}4x-3y=0\\\\-2x+2y=-1\end{cases}
⎩
⎪
⎪
⎨
⎪
⎪
⎧
​

4x−3y=0
−2x+2y=−1

1) How can we get System BBB from System AAA?
Choose 1 answer:

(Choice A, Checked, Correct)
CORRECT (SELECTED)
Replace one equation with the sum/difference of both equations

(Choice B, Incorrect)
INCORRECT
Replace only the left-hand side of one equation with the sum/difference of the left-hand sides of both equations

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

2) Based on the previous answer, are the systems equivalent? In other words, do they have the same solution?
CORRECT (SELECTED)
Yes

Respuesta :

facundo3141592

For the given systems A and B:

1) Replace the first equation of A by the sum between the two equations of A.

2) Yes, the systems are equivalent.

How to get system B from system A?

Here we have the two systems of equations:

A:

6x - 5y = 1

-2x + 2y = -1

B:

4x - 3y = 0

-2x + 2y = -1

The second equation is the same in both systems, so we only look at the first equations.

In A we have:

6x - 5y = 1

If we add the second equation of A, then we get:

(6x - 5y) + (-2x + 2y) = 1 + (-1)

4x - 3y = 0

This is the first equation of B.

Then we need to replace the first equation by the sum between the first and second equations.

2) Are the systems equivalent?

Yes, because we did not "modify" system A, we just rewrite it and we got system B, then both systems have the same solutions.

If you want to learn more about systems of equations:

https://brainly.com/question/847634

#SPJ1