Which equation can pair with 3x + 4y = 8 to create a consistent and independent system?
6x + 8y = 16
–3x – 4y = –6
6x – 3y = 2
–3x – 4y = –8

The equation that will result in a consistent and independent system is:

Step-by-step explanation:

The linear equation is given by:

Now, we are asked to find a equation such that the system will be consistent and independent.

a)

on dividing by on both side of the equation we get:

Since, both the equations are equal.

Hence, the system is dependent.

b)

On multiplying both side of the equation by -1 we get:

The graph of this system of equation are parallel lines.

Hence, the system is inconsistent.

c)

On multiplying the given equation i.e. equation (1) by 2 and subtracting with this equation we get:

and putting the value of y in equation (1) we get:

Hence, we get a unique solution.

This means that the system is consistent and independent.

d)

On multiplying both side of the equation by -1 we get:

Hence, the system is dependent.

( Since both the equations will  be same )