Question

5x-2y=-24
-4y=-48-10x if the system cannot be solved state that it cannot be solved and explain why

Answer 1

let's do a little rearranging on that second equation:

5x-2y=-24
10x-4y=-48

now divide the second equation by 2

what are the two equations now?

Answer 2

the second row or the whole thing divide by 2?

Answer 3

second "row" I suppose
not the first equation, only the second

but then write then both out again after so you can compare them

Answer 4

ok hold on

Answer 5

would it be 5x-2=-24 and the other 1 is 5x-2=-24

Answer 6

you dropped the y
write them one over the other; it's more clear that way

Answer 7

5x-2y=-24
5x-2y=-24

hm... they are both the same

what does that mean for the solutions?

Answer 8

that it doesnt have 1?

Answer 9

if there is no solution, this system should lead to a contradiction
let's see if that's true...

Answer 10

but i have a question y did u divide by 2? like how did u know?

Answer 11

I noticed that the first equation is a multiple of the second
you should always look for that kind of thing in systems

ask yourself
"what can I multiply these equations by in order to get rid of (at least) one of the variables"

it does take a little practice to recognize these things of course

Answer 12

so back to where we were:

5x-2y=-24
5x-2y=-24

do the same as before and subtract one equation from the other
make sure to write out both sides

what do you get by subtracting one eqn from the other

Answer 13

like just subtract dont multiply

Answer 14

just subtract the second equation from the first

keep the left and right sides of the equations separate, as we did in the last problem

Answer 15

if i just subtract both of them i get 5x-2y=-72 am i right?

Answer 16

not quite, be careful with those negative signs
and don't forget to subtract the left side as well; that is essential

5x-2y=-24
5x-2y=-24
-----------
5x-2y-(5x-2y)=-24-(-24)
^^^simplify both sides

Answer 17

ok so it would be 0? right

Answer 18

careful:
write out both sides or else that tells you nothing about the solutions

Answer 19

that = sign can't just disappear like that

Answer 20

so wat would it be?

Answer 21

what is on the left ?
5x-2y-(5x-2y)=?

Answer 22

10x and 4y?

Answer 23

5x-2y-(5x-2y)=5x-2y-5x+2y=0

what about the other side?

Answer 24

it would be 0 too

Answer 25

so then we can write
0=0
that's what I wanted from you, because now I get to ask you:
how often is that statement true?

Answer 26

o lol the statement but it doesnt have a solution right?

Answer 27

0=0 is \(always\) true
that means that there are \(infinite\) solutions

whenever the system can be reduced to a contradiction, like 1=2
then there are no solutions

whenever we can reduce the system to something that is always true, like 1=1
then there are infinite soutions

Answer 28

solutions*

Answer 29

ooo ok i get it thank you soo much ur really good in explaining :)

Answer 30

thanks I try
and thanks for listening :)

Answer 31

well ur doing good ;) thnx