Question

Which equation is written in standard form?
3x + 4x = 14
© y-5 =-2x+4)
© 7x + 3y - 21
y = -2x + 3

Answer 1

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:

1. **\( 3x + 4x = 14 \)**
- This can be simplified to \( 7x = 14 \), which can be rewritten as \( 7x + 0y = 14 \).
- This is in standard form.

2. **\( y - 5 = -2x + 4 \)**
- Rearranging gives \( 2x + y = 9 \). This is in standard form.

3. **\( 7x + 3y - 21 \)**
- This equation can be written as \( 7x + 3y = 21 \). This is also in standard form.

4. **\( y = -2x + 3 \)**
- 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 **\( 7x + 3y = 21 \)**.