Question

Write the following in general form:
Y=3x-7
Y=3+x/4
5x=2y-1

Answer 1

To write the given equations in general form, we need to rearrange each equation into the form \(Ax + By + C = 0\), where \(A\), \(B\), and \(C\) are integers.

1. **Equation 1: \(Y = 3x - 7\)**

Rearranging:
\[
3x - Y - 7 = 0
\]
General Form:
\[
3x - Y - 7 = 0 \quad \text{or} \quad 3x - Y = 7
\]

2. **Equation 2: \(Y = 3 + \frac{x}{4}\)**

Rearranging:
\[
Y - \frac{x}{4} - 3 = 0
\]
To eliminate the fraction, multiply by 4:
\[
4Y - x - 12 = 0
\]
General Form:
\[
-x + 4Y - 12 = 0 \quad \text{or} \quad x - 4Y + 12 = 0
\]

3. **Equation 3: \(5x = 2y - 1\)**

Rearranging:
\[
5x - 2y + 1 = 0
\]
General Form:
\[
5x - 2y + 1 = 0
\]

Putting all equations together, we get:

1. \(3x - Y - 7 = 0\) (or \(3x - Y = 7\))
2. \(x - 4Y + 12 = 0\)
3. \(5x - 2y + 1 = 0\)