# Which equation can pair with 3x + 4y = 8 to create a consistent and independent system?

The given question is based on the nature of solutions of a system of simultaneous linear equations.

## Answer: Ax + By = C with 4A ≠ 3B can be paired with 3x + 4y = 8 to create a consistent and independent system. Example: 5x + 8y = 12.

Let us explore more about the consistent and independent system or unique solution case of the system of linear equations.

**Explanation:**

A system of two linear equations:

\((a)_{1}\)x + \((b)_{1}\)y + \((c)_{1}\)_{ }= 0 and \((a)_{2}\)x + \((b)_{2}\)y + \((c)_{2}\)_{ }= 0 is said to be a consistent and independent system if and only if \((a)_{1}\)/\((a)_{2}\)_{ }≠ \((b)_{1}\)/\((b)_{2}\)

Given 3x + 4y = 8 ⇒ \((a)_{1}\)_{ }= 3 , \((b)_{1}\)_{ }= 4, \((c)_{1}\) = 8

For a system of linear equations to be a consistent and independent system \((a)_{1}\)/\((a)_{2}\)_{ }≠ \((b)_{1}\)/\((b)_{2}\)

⇒ \((a)_{1}\)/\((b)_{1}\)_{ }≠ \((a)_{2}\)/\((b)_{2}\)

⇒ \((a)_{2}\)/\((b)_{2}\) ≠ 3/4

⇒ \((a)_{2}\)/\((b)_{2}\) can be 5/8 or 3/5 or any fraction which is not an equivalent fraction of 3/4.