If one equation of a pair of dependent linear equations is -3x+5y-2=0. The second equation will be:

Options

A. `-6x+10y-4=0`
B. `6x+10y-4=0`
C. `6x-10y-4=0`
D. `-6x+10y+=0`

Answer

To find the second equation of a pair of dependent linear equations given the first equation as \(-3x + 5y - 2 = 0\), we need to understand that dependent linear equations are essentially multiples of each other.

### Step-by-step Solution:

1. **Identify the coefficients of the given equation**:
The given equation is \(-3x + 5y - 2 = 0\).
- Coefficient of \(x\) (a1) = -3
- Coefficient of \(y\) (b1) = 5
- Constant term (c1) = -2

2. **Set up the relationship for dependent equations**:
For two equations to be dependent, the ratios of their coefficients must be equal:
\[ \frac{a1}{a2} = \frac{b1}{b2} = \frac{c1}{c2} = k \]
Here, \(a2\), \(b2\), and \(c2\) are the coefficients of the second equation, and \(k\) is a constant.

3. **Express the coefficients of the second equation in terms of \(k\)**:
- Let \(a2 = -3k\)
- Let \(b2 = 5k\)
- Let \(c2 = -2k\)

4. **Formulate the second equation**:
The second equation can be formed as:
\[ a2x + b2y + c2 = 0 \]
Substituting the values:
\[ -3kx + 5ky - 2k = 0 \]

5. **Choose a value for \(k\)**:
To find a specific second equation, we can choose a value for \(k\). A common choice is \(k = 2\):
\[ a2 = -3(2) = -6 \]
\[ b2 = 5(2) = 10 \]
\[ c2 = -2(2) = -4 \]

6. **Write the second equation**:
Substituting these values back into the equation gives:
\[ -6x + 10y - 4 = 0 \]

### Final Answer:
The second equation of the pair of dependent linear equations is:
\[ -6x + 10y - 4 = 0 \]