The dependent pair of linear equations is always:

Options

A. Inconsistent
B. Parallel
C. Straight
D. Consistent

Answer

To solve the question regarding the nature of a dependent pair of linear equations, we will analyze the definitions and properties of linear equations step by step.

### Step-by-Step Solution:

1. **Understanding Linear Equations**:
- A linear equation in two variables can be represented in the form \(Ax + By + C = 0\), where \(A\), \(B\), and \(C\) are constants, and \(x\) and \(y\) are variables.

**Hint**: Recall that linear equations represent straight lines when graphed on a coordinate plane.

2. **Types of Linear Equation Pairs**:
- There are three types of pairs of linear equations:
- **Consistent**: The equations have at least one solution (the lines intersect at one point).
- **Inconsistent**: The equations have no solutions (the lines are parallel).
- **Dependent**: The equations have infinitely many solutions (the lines coincide).

**Hint**: Think about how the lines behave when graphed: do they meet, never meet, or lie on top of each other?

3. **Defining Dependent Equations**:
- A dependent pair of linear equations means that one equation is a multiple of the other. This results in the two lines being the same line, hence they coincide.

**Hint**: If you can express one equation as a scalar multiple of the other, they are dependent.

4. **Conclusion**:
- Since dependent equations coincide, they have infinitely many solutions. Therefore, they are considered consistent because consistent equations can either intersect at one point or coincide (which is the case for dependent equations).

**Hint**: Remember that "consistent" means there is at least one solution, and in the case of dependent equations, there are infinitely many solutions.

### Final Answer:
The dependent pair of linear equations is always **consistent**.