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

a.) 6x+8y=16
b.) -3x-4y=-6
c.) 6x-3y=2
d.) -3x-4y=-8

The right answer is C)

Consistent and independent system of two linear equations is a system such that there is only one solution for the system, that is, the two straight lines cross at a point. So we can analyze each case and I have attached some graphs to provided you with examples. Those graphs aren't about the equations but it's about general cases:

A) Consistent and dependent. If we divide this given equation by 2 we get the same line. (See Figure 1)

B) Inconsistent. No solutions. (See Figure 2)

C) Consistent and Independent. (See Figure 3)

D) Consistent and dependent. If we multiply this equation by -1 we get the same line. (See Figure 1)