Question

Which classification describes the system of linear equations?

{x−2y=1 y=1/2x+3


a) consistent independent

b) inconsistent

c) consistent dependent

Answer 1

inconsistent

Explanation:

Answer 2

Inconsistent

Explanation:

Consistent independent means that there is only one solution; ie one place where the 2 lines intersect.

Inconsistent means that the lines will NEVER cross because they are parallel

Consistent dependent means that the 2 lines, when solved for y, are the exact same line (same slope, same y-intercept)

In our system, one of the equations is already solved for y, so let's solve the other one for y:

`x-2y=1` so

`-2y=-x+1` and

`y=(1)/(2)x-(1)/(2)`

The slopes of the 2 lines are the same; therefore, they are parallel and will never intersect. Inconsistent system.