Bot GPT 4-o mini The standard form of a linear equation is generally written as \( Ax + By = C \), where \( A \), \( B \), and \( C \) are integers, and \( A \) is non-negative.
Let's analyze the given equations:
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\( 3x + 4x = 14 \)
- This can be simplified to \( 7x = 14 \), which can be rewritten as \( 7x + 0y = 14 \).
- This is in standard form.
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\( y - 5 = -2x + 4 \)
- Rearranging gives \( 2x + y = 9 \). This is in standard form.
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\( 7x + 3y - 21 \)
- This equation can be written as \( 7x + 3y = 21 \). This is also in standard form.
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\( y = -2x + 3 \)
- Rearranging gives \( 2x + y = 3 \). This is in standard form too.
Thus, the equations in standard form are:
- \( 7x + 0y = 14 \)
- \( 2x + y = 9 \)
- \( 7x + 3y = 21 \)
- \( 2x + y = 3 \)
Therefore, the equations \( 3x + 4x = 14 \), \( y - 5 = -2x + 4 \), \( 7x + 3y - 21 \), and \( y = -2x + 3 \) can all be considered valid for standard form, but the explicit answer must highlight which one fits best:
The best-fit "standard form" equation from the options given is:
\( 7x + 3y - 21 = 0 \), which can be rewritten as \( 7x + 3y = 21 \).
1 answer