Question

plz help :( will give medal :)!<3

Several systems of equations are given below.

System 1
y = 6x – 1.5
y = –6x + 1.5

System 1
x + 3y = –6
2x + 6y = 3

System 1
2x –y = 5
6x – 3y = 15


Which system of equations is consistent-independent? How many solutions will the system of equations have? Expain your answers.
Which system of equations is consistent-dependent? How many solutions will the system of equations have? Expain your answers.
Which system of equations is inconsistent-independent? How many solutions will the system of equations have? Expain your answers

Answer 1

Each equation makes a rule. two simultaneous rules can
a) make clear the only possible double-solution.
b) have the same dependance to some variable..
c) contradict each other.

Answer 2

are you familiar with elimination in systems of equations?

Answer 3

a=intersecting lines / number of solution
b=same line / many solution
c=paraelle line / no solution

Answer 4

yes ive learned it

Answer 5

YES :) very true
also

a- consistent-independent
b- consistent-dependent
c- inconsistent-independent

inconsistent: contradiction
dependent: same line, same dependence

Answer 6

y = 6x – 1.5
y = –6x + 1.5
wat do i do from here??

Answer 7

graphing would be best, this is the first graph

Answer 8

https://www.desmos.com/calculator

Answer 9

thanks, that's a great graphing calculator :)

Answer 10

haha thank ! : )np

Answer 11

for the second graph, I re-arranged the variables like this:
y = -2 -1/3 x
y = 1/2 - 1/3 x

Answer 12

x + 3y = –6 -2(x+3y=-6)? -->
2x + 6y = 3

Answer 13

yes then can eliminate:

-2x -6y = -6
2x + 6y = +3
--------------
0 + 0 = -3 CONTRADICTION

Answer 14

x + 3y = –6 -2(x+3y=-6)? --> -2x-6=12?

Answer 15

true, it should be 12

-2x -6y = 12
2x + 6y = +3
--------------
0 + 0 = +15 CONTRADICTION

the lines of the equations in the second system are parallel and always
contradict each other for any variable x

Answer 16

i dont need to graph it?

Answer 17

well you don't really have to, contradiction means they must be parallel
can enter it into the graphic calculator nonetheless to double check

Answer 18

mhhh i see ! : )

Answer 19

2x –y = 5 <--(-3)--> (-6x+3y=-15) : D
6x – 3y = 15

Answer 20

0 + 0 = 0, right?

it's the exact same equation, once with factor 1
and once with factor 3

Answer 21

it doesn't matter what x you choose, since they're compensated anyway

Answer 22

yes o.o does that mean its B o.o

Answer 23

yes :) it's B) -
consistent (0 = 0) and dependent (on x: infinite solutions)

Answer 24

wow that was kinda easy hehe ^_^ thanks so much for using your time with me !

Answer 25

you're welcome