solve y=2x+1 and 2y-4x= -6. Are they consistent or inconsistent, dependent or independent?

Answer 1

First: replace 2x+1 with the "y" variable in the 2nd equation.

2(2x + 1) - 4x = - 6

*Eliminate the parenthesis by multiplying the outer term with the terms in parenthesis (Distribution Property).

2(2x) + 2(1) - 4x = - 6

4x + 2 - 4x = - 6

*Combine "like" terms.

4x - 4x + 2 = - 6

2 = - 6

False

Since the solution is false (2 doesn't equal - 6), the equations are inconsistent.

Answer 2

Rewrite the 2nd equation as

2y = 4x - 6
y = 2x - 3

The equations have the same slope but different y intercepts, so the lines are parallel, which makes them inconsistent.

Answer 3

the lines are parallel so there is no answer (inconsistent)