Question

5x - y = 8
Part A- Explain how you will show all of the solutions that satisfy this equation.
Part B-
determine 3 different solutions for this equation.

Part C- Write an equation that can be paired with the given equation in order to form a system of equations that is inconsistent.
@undeadknight26

Answer 1

@phi @SolomonZelman

Answer 2

Hey Brie :)
Mmmm I'm not exactly sure what they're asking for in part A,
maybe they want us to write it in terms of y= stuff.

Let's start with part B though.
Do you understand how to find solutions?
Like if you let x=0,

5x - y = 8 becomes,
0 - y = 8

What y value does that give us?

Answer 3

@StudyGurl14

Answer 4

i prefer Alex lol and no im so freakign tired and done with this test i cant even see straight can you dumb it up for me please?

Answer 5

oh 8 right?

Answer 6

This is given to us in the `standard form of a line`,\[\Large\rm 5x - y = 8\]
So we have a line :)
We can pick any point for one of our letters, and figure out what the other point is.

So by choosing x=0,\[\Large\rm 5\cdot 0-y=8\]\[\Large\rm -y=8\]Multiply both sides by -1,\[\Large\rm y=-8\]

This is telling us that one solution to the given equation is \(\Large\rm (0,-8)\)

Answer 7

8 is close though ^^ hehe

Answer 8

If we choose to let y=0,
this will lead us to another solution.
(zeros are easy to work with, so they're nice numbers to choose.)

Answer 9

okieeeeee you have my full attention

Answer 10

\[\Large\rm 5x-y=8\]\[\Large\rm 5x-0=8\]\[\Large\rm 5x=8\]Divide by 5, giving us,\[\Large\rm x=\frac{8}{5}\]So that gives us our next solution, \(\Large\rm \left(\dfrac{8}{5},0\right)\).

Answer 11

Realize that this is a line,
there will be an infinite number of solutions.
We're just choosing the ones that are easy.

Answer 12

ok and then there is one more right?

Answer 13

There are infinitely many more.
But yes we need just one more :)

How about if x=2?
Can you figure out the y that goes along with that?

Answer 14

oh lordy let me try

Answer 15

10-y=8?
then y would equal 6?

Answer 16

10 - 6 = 8 ? 0_o

Oh boy, you really are tired, huh?

Answer 17

ya

Answer 18

How far apart are 10 and 8? -_-
If you subtract 6 from 10, you end up at 4, not at 8 like we need.

Answer 19

sorry y would be 12

Answer 20

whut? :U
brie brie brie.....

Answer 21

You're at 10....
you need to subtract some amount to get to 8.

So you would subtract.... 2, yes?

10
minus
2
is
8

Yes? 0_o

Answer 22

omg I told you I was tired I cant think sorry

Answer 23

So when we chose x=2,
we ended up with a y value of 2 as well.
Do you understand how to write that as a coordinate pair?

Answer 24

When x=0,
we found our y to be -8.
And we wrote it as (0,-8).

How bout this third solution? How we gonna write it? :U

Answer 25

I really don tknow im so sorry

Answer 26

Mmmm k, moving on :U

For Part C:
In order for a system to be `incosistent`, it means that the system has `no solutions`.
This happens when lines are `parallel` but have different `y-intercepts`.

\(\Large\rm 5x-y=8\)
We'll multiply our x and y by some amount,
then throw a different number on the right side.

If we multiplied by 2,\[\Large\rm 10x-2y=16\]And throw a different number on the right side,\[\Large\rm 10x-2y=10\]This gives us, with the first equation we were given, a system this is inconsistent.
\[\Large\rm inconsistent\quad \cases{5x-y&=8\\ \rm 10x-2y&=10}\]

Answer 27

Ok your brain must be fried by now.
Go eat some pringles, then go to bed! :)

Answer 28

pringles?

Answer 29

Yah, it's a brand of... chips.. or whatever XD

Answer 30

so wait what was the last solution ? @zepdrix

Answer 31

WOW you reply right after I submit my exam -_-

Answer 32

Our last solution? :U
Comeoooooon, don't be a slacker.
You gotta contribute something here :(

Our first solution was given by x=0, y=-8,
so we wrote our coordinate pair (x,y) as (0,-8).

Our second solution was x=8/5, y=0,
so we wrote our coordinate pair (x,y) as (8/5, 0).

Our third solution was x=2, y=2,
so we would write our coordinate pair (x,y) as ?

Answer 33

You have to contribute something brie :(
I can't just do the entire assignment for you..