Which Equation Can Pair With 3x + 4y = 8 to Create a Consistent and Independent System?


Question: 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:

a1x + b1y + c= 0 and a2x + b2y + c= 0 is said to be a consistent and independent system if and only if a1/a≠ b1/b2

Given 3x + 4y = 8 ⇒ a= 3 , b= 4, c1 = 8

For a system of linear equations to be a consistent and independent system a1/a≠ b1/b2

⇒ a1/b≠ a2/b2

⇒ a2/b2 ≠ 3/4

⇒ a2/b2 can be 5/8 or 3/5 or any fraction which is not an equivalent fraction of 3/4.

Thus, 5x + 8y = 12 or any equation of form Ax + By = C with 4A ≠ 3B can be paired with 3x + 4y = 8 to create a consistent and independent system.