Question

Is the following system consistent or inconsistent?

Answer 1

8x + y + 4 = 0
y = -8x - 4

Answer 2

it is consistent, if it has atleast one solution

Answer 3

so do i just plug the y in and try to solve it?

Answer 4

find out how many solutions it can have, by watever method u want :)

Answer 5

i got 0 = 0... what the heck does that mean

Answer 6

left side = right side

that means, infinite solutions !

Answer 7

both equations are one and same !!

Answer 8

how do i solve one like this:
-2x - 2y = 6
10x + 10y = -30

Answer 9

simplify the equations first

Answer 10

i'm really bad at that when there's a coefficient higher than 1 in front of the variables

Answer 11

so, make the coefficient 1 :)

divide -2 in first equation
divide 10 in second equation

Answer 12

first equation :-

-2x - 2y = 6

divide -2 both sides
-2x - 2y = 6
/-2 /-2

x + y = -3 -----------(1)

Answer 13

x + y = -3
x + y = -3

Answer 14

one of them is x - y = -3*****

Answer 15

both are x+y = -3

Answer 16

okay so now what

Answer 17

that means both are same equations eh ?

Answer 18

so no solution?

Answer 19

so, infinite solutions

Answer 20

oohhh

Answer 21

if u solve them, u wud get 0 = 0

Answer 22

i have one last question. what do i do for one that is like
2y = x - 7
-2x - 6y = -14

Answer 23

solve it and see

Answer 24

2y = x - 7
x + 3y = 7

Answer 25

now what

Answer 26

solve them

Answer 27

how..

Answer 28

2y = x - 7
x + 3y = 7

Answer 29

solve y from first equation, and substitute it in second equation

Answer 30

i don't know how i'm supposed to divide 2 into that entire first equation and then try and solve it.

Answer 31

i'm gonna get weird numbers

Answer 32

you're on right track, do it :)

Answer 33

2y = x - 7

y = (x-7)/2

Answer 34

substitute this value for y in 2nd equation

Answer 35

\[x + 3 = (\frac{ x }{ 2 } - \frac{ 7 }{ 2 } ) = 7\]

Answer 36

i don't know how to do the rest.

Answer 37

u mean

\(\large x + 3(\frac{ x }{ 2 } - \frac{ 7 }{ 2 } ) = 7 \)

?

Answer 38

u dont have to solve it completely, u can see it x will certainly have some value

Answer 39

so that means, the system will have ONE unique solution
so the system is consistent