Question

Without graphing, is the system independent, dependent, or inconsistent?
y=2x-8
2x-y=8

Answer 1

rearrange the 2nd equation until it's in the same form as the first...
The first has y on the left and x and the constant on the right.

So, on the 2nd equation:
2x - y = 8
2x - 2x - y = 8 - 2x <<--- subtract 2x from both sides
- y = 8 - 2x <<-- simplify
(-1)(-y) = (-1)(8 -2x) <<--- mult both sides by neg 1 to change -y to y on left
y = 2x - 8 <<--- simplify

Notice that this equation is exactly the same as equation # 1. I believe that makes it dependent, but you need to check your definitions.

Answer 2

yup, you are right!so if they are dependent they have many solutions

Answer 3

ok, great :)

What that means is that if you were to graph a single line, and then draw the same line again exactly, all solutions of one line satisfy the other line also (because they're the same!!)

When solutions are independent, they look like 2 lines that cross... the intersection point is the single solution.

Answer 4

thank you so much you helped alot! (: