Question

Use the table to answer the question.

System A System B
3x−y=−1

−3x−y=5

3x−y=−1

?

Which of the following terms will make the systems equivalent?


(1 point)
Responses

9x+3y=−15
9 x plus 3 y equals negative 15

3x+9y=−15
3 x plus 9 y equals negative 15

6x−2y=4
6 x minus 2 y equals 4

−6x−2y=4

Answer 1

To determine which of the given equations will make the systems equivalent, we need to manipulate the equation \(3x - y = -1\) of System A to see if it can be expressed in a form that matches any of the options provided.

Starting with the equation \(3x - y = -1\), we can multiply both sides by a constant. If we multiply both sides by 3, we get:

\[
3(3x - y) = 3(-1)
\]
\[
9x - 3y = -3
\]

Now, we can solve for \(y\):

\[
-3y = -9x - 3
\]
\[
y = 3x + 1
\]

However, we are looking for equivalent equations. Instead of manipulating the equations, let's check the options provided:

1. \(9x + 3y = -15\): We can rearrange it:
\[
3y = -9x - 15 \implies y = -3x - 5 \quad (\text{not equivalent})
\]

2. \(3x + 9y = -15\): Rearranging gives:
\[
9y = -3x - 15 \implies y = -\frac{1}{3}x - \frac{5}{3} \quad (\text{not equivalent})
\]

3. \(6x - 2y = 4\): Rearranging gives:
\[
-2y = -6x + 4 \implies y = 3x - 2 \quad (\text{not equivalent})
\]

4. \(-6x - 2y = 4\): Rearranging gives:
\[
-2y = 6x + 4 \implies y = -3x - 2 \quad (\text{not equivalent})
\]

None of the direct rearrangements produce an equivalent expression immediately, but let's look for scaling of the original \(3x - y = -1\):

When we multiply both sides of \(3x - y = -1\) by -3:

\[
-3(3x - y) = -3(-1)
\]
\[
-9x + 3y = 3 \implies 9x - 3y = -3 \quad (which is a form of number 1 when expressed correctly).

Now that we notice option 1 can be equivalent under certain scaling, we further confirm if multiplying it accordingly works out.

However, I suggest re-evaluating the initial target equation comparing all values directly.

Ultimately, by process of finding equivalent terms under multiplication and observation, **none** are directly equivalent to our first equations across rearrangement checks!

Thus, the **correct answer is not immediately given**. The identification of necessary scaling yields other non-factors and substantial equations lead one back toward validating parallel setups typically classified.

Reviewing remains needed as noted, though equivalent tracking shifted bases does exist in structure albeit if anything becomes cleaner for re-definition.