Question
the table to answer the question.
System A
System B
7x + 4y = -4
5x + 8y = 28
7x + 4y = -4
?
Which of the following terms will make the systems equivalent?
(1 point)
0-14x - 8y = 8
0 -14x - 8y = -8
• 12x + 12y = 24
-12x - 12y = 24
System A
System B
7x + 4y = -4
5x + 8y = 28
7x + 4y = -4
?
Which of the following terms will make the systems equivalent?
(1 point)
0-14x - 8y = 8
0 -14x - 8y = -8
• 12x + 12y = 24
-12x - 12y = 24
Answers
GPT-4o mini
To determine which equation will make the systems equivalent, we need to analyze the first system and see what modifications will keep the second system equivalent.
The equations in System A are:
1. \( 7x + 4y = -4 \) (which is already given)
2. \( 5x + 8y = 28 \) (which is the second equation)
The first equation of System B is the same as System A:
1. \( 7x + 4y = -4 \)
2. We need to find an equivalent equation for \( 5x + 8y = 28 \).
First, let’s rewrite \( 5x + 8y = 28 \) to see if we can manipulate this:
We can express \( 5x + 8y = 28 \) in terms of its equivalent form. To find an equivalent expression, we can multiply the entire equation by a non-zero constant.
The equation \( 5x + 8y = 28 \) can be rewritten in several equivalent forms. Here's a quick check using multiplication by -2:
-2(5x + 8y) = -2(28)
This gives us:
-10x - 16y = -56.
Now, we can check the provided options for equivalence. The options provided were:
1. \( 0 - 14x - 8y = 8 \)
2. \( 0 - 14x - 8y = -8 \)
3. \( 12x + 12y = 24 \)
4. \( -12x - 12y = 24 \)
1 and 2 do not match the form of our equation since they both differ in coefficients.
Let’s take a closer look at option 3:
\( 12x + 12y = 24 \)
This can be manipulated to see if it can somehow relate to the original second equation we have \( 5x + 8y = 28 \). But seeing this form makes it evidently different.
Lastly, we also run through option 4:
\( -12x - 12y = 24 \)
None of these equations appear to relate back sufficiently to \( 5x + 8y = 28 \) or can be deduced as equivalent without additional scaling.
To find the equivalent equation in relation to the second system, the most appropriate would typically include aligning coefficients or manipulation of the original equations accurately.
Let’s define the second equation by re-evaluating multiplication or adjustments to align as expected rather than through arbitrary transition.
After deliberating each answer and through trial,
None of the provided options offers a correct equivalent relationship that can replace \( 5x + 8y = 28 \) without further transformations. If confirmation to equivalency is necessary, proceed with multiplication of 5 and adjust instead to retain forms recognizable through linear transformations.
In conclusion, after evaluating all options, none of them will form an equivalent relation properly for \( 5x + 8y = 28 \).
If forced to choose, closer format should advise on option format recognition directly rather than through introduction typically displacing original relational states. If further discussions is needed, I'd be happy to clarify or assist.
The equations in System A are:
1. \( 7x + 4y = -4 \) (which is already given)
2. \( 5x + 8y = 28 \) (which is the second equation)
The first equation of System B is the same as System A:
1. \( 7x + 4y = -4 \)
2. We need to find an equivalent equation for \( 5x + 8y = 28 \).
First, let’s rewrite \( 5x + 8y = 28 \) to see if we can manipulate this:
We can express \( 5x + 8y = 28 \) in terms of its equivalent form. To find an equivalent expression, we can multiply the entire equation by a non-zero constant.
The equation \( 5x + 8y = 28 \) can be rewritten in several equivalent forms. Here's a quick check using multiplication by -2:
-2(5x + 8y) = -2(28)
This gives us:
-10x - 16y = -56.
Now, we can check the provided options for equivalence. The options provided were:
1. \( 0 - 14x - 8y = 8 \)
2. \( 0 - 14x - 8y = -8 \)
3. \( 12x + 12y = 24 \)
4. \( -12x - 12y = 24 \)
1 and 2 do not match the form of our equation since they both differ in coefficients.
Let’s take a closer look at option 3:
\( 12x + 12y = 24 \)
This can be manipulated to see if it can somehow relate to the original second equation we have \( 5x + 8y = 28 \). But seeing this form makes it evidently different.
Lastly, we also run through option 4:
\( -12x - 12y = 24 \)
None of these equations appear to relate back sufficiently to \( 5x + 8y = 28 \) or can be deduced as equivalent without additional scaling.
To find the equivalent equation in relation to the second system, the most appropriate would typically include aligning coefficients or manipulation of the original equations accurately.
Let’s define the second equation by re-evaluating multiplication or adjustments to align as expected rather than through arbitrary transition.
After deliberating each answer and through trial,
None of the provided options offers a correct equivalent relationship that can replace \( 5x + 8y = 28 \) without further transformations. If confirmation to equivalency is necessary, proceed with multiplication of 5 and adjust instead to retain forms recognizable through linear transformations.
In conclusion, after evaluating all options, none of them will form an equivalent relation properly for \( 5x + 8y = 28 \).
If forced to choose, closer format should advise on option format recognition directly rather than through introduction typically displacing original relational states. If further discussions is needed, I'd be happy to clarify or assist.