solve: x-5/3=x-3/5

This equation has no solution: 
x-5/3=x-3/5 
x-x-5/3=x-x-3/5 

-5/3=-3/5 which is clearly not true. Whenever we can simplify an equation enough to determine that it will always be false, we know that the equation has no solution. 

:)

Types of solutions

9) Chose A, B, or C from the list below. 4x+2y=8 Y=4-2x A) Inconsistent B) Consistent & Dependent C) Consistent & Independent

If we add 2x to both sides of the lower equation then double each of it's terms we'll get the upper equation. These lines both have the same solution, so the system is consistent and dependent.

:)

Linear systems of equations

7) Chose A, B, or C from the list below. Y=3x-5 Y=3x+6 A) Inconsistent B) Consistent & Dependent C) Consistent & Independent

Your Answer:

both equations have the same slope, but different y-intercepts, so they will never intersect. This system is inconsistent.


:)