Which classification describes the system of linear equations? {x−2y=1 y=1/2x+3 a) consistent independent b) inconsistent c) consistent dependent

Inconsistent

Step-by-step 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:

so

and

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

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.