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).