Question

Question
Use the table to answer the question.

System A System B
2x−3y=−24

x+6y=18

2x−3y=−24

2x+12y=36

True or false: The systems in the table are equivalent. Enter 1 for true or 2 for false.

(1 point)
Remaining Attempts : 3
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Answer 1

To determine if the systems in the table are equivalent, we need to analyze the equations in both systems.

**System A:**
1. \(2x - 3y = -24\)
2. \(x + 6y = 18\)

**System B:**
1. \(2x - 3y = -24\)
2. \(2x + 12y = 36\)

Now, we can see that the first equation in both systems is the same: \(2x - 3y = -24\).

Next, let's evaluate the second equations of both systems:

1. **For System A:**
\(x + 6y = 18\)

2. **For System B:**
\(2x + 12y = 36\)

Now we can see if \(x + 6y = 18\) is equivalent to \(2x + 12y = 36\).

To compare them, we can multiply the first equation by 2:

Multiply \(x + 6y = 18\) by 2:

\[
2(x + 6y) = 2(18) \\
2x + 12y = 36
\]

As we can see, after multiplying the first equation of System A by 2, we obtain the second equation of System B.

Since both equations represent the same lines in the coordinate plane, this confirms that the systems are equivalent.

Thus, the statement is **True**.

So the answer is: **1** (True).