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System AAA \text{\quad}start text, end text System BBB
\begin{cases}-3x+12y=15\\\\7x-10y=-2\end{cases}
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−3x+12y=15
7x−10y=−2
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\begin{cases}-x+4y=5\\\\7x-10y=-2\end{cases}
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−x+4y=5
7x−10y=−2
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1) How can we get System BBB from System AAA?

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

Respuesta :

facundo3141592

For systems A and B we have:

1) Change the first equation in A by a multiple of itself. (the multiple is 1/3).

2) Yes, the systems are equivalent.

How to get system B from system A?

Here we have the systems of equations:

A:

-3x + 12y = 15

7x - 10y = -2

B:

-x + 4y = 5

7x - 10y = -2

Notice that the second equation is the same in both systems, so we only need to work with the first ones.

If we take the first equation in system A:

-3x + 12y = 15

If we divide both sides by 3, we get:

-x + 4y = 5

Which is the first equation of B.

So we just need to replace the first equation in system A by a multiple of itself to get system B.

Because of that, we conclude that both systems are equivalent (because are made of the same equations) which means that both systems have the same solutions.

If you want to learn more about systems of equations:

https://brainly.com/question/847634

#SPJ1

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