Which system of equations is equivalent to this system?
6x + 4y = 12
3x + y = 8
4x + 4y = 48
3x + y = 8
-4x + 4y = 48
3x + y = 8
2x + 4y = 12
3x + y = 8
Which system of equations is equivalent to this system?
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To determine which system of equations is equivalent to the original system, we can manipulate the equations mathematically to see if they can be transformed to match the original equations.
The original system is:
1. (6x + 4y = 12)
2. (3x + y = 8)
Let’s analyze the first equation in the options:
1. Option 1:
(4x + 4y = 48) can be simplified by dividing the entire equation by 4, which yields:
(x + y = 12). This does not match anything in the original system.
2. Option 2:
(-4x + 4y = 48) can be simplified by dividing by -4, yielding:
(x – y = -12), which again does not match.
3. Option 3:
(2x + 4y = 12). Dividing the entire equation by 2 gives:
(x + 2y = 6). Upon solving, this does not yield a substitute for both original equations.
4. Option 4:
The second equation (3x + y = 8) remains unchanged and is part of the original system.
Looking at the first equation of the original system, we can see that when reduced, it should yield coefficients consistent with the equivalent form of the