Question

Please Help
Solve the following system of equations:

-2x + y = 1
-4x + y = -1

(3, 1)

(-1, 3)

(-1, -3)

(1, 3)

Answer 1

what is the the difference between the equations ?

Answer 2

-2x and =4x 1 and -1

Answer 3

what is -2x - 4x = ?

what is 1 - (-1) = ??

Answer 4

-6x and 2

Answer 5

whops

i meant -2x - (-4x) - ?

Answer 6

-2x + y = 1
-4x + y = -1

the difference between the left hand sides of the equations




are
(-2x + y) - (-4x + y)

= -2x + y + 4x - y

= -2x + 4x

= ?

Answer 7

okay 6x

Answer 8

= (-2 + 4)x
=?

Answer 9

you already got the difference between the right hand sides

1 - (-1)
= 1+1
= 2

Answer 10

Oh, didn't see the negative lol
= (-2+4)x =2x

Answer 11

so the difference between the two equation
-2x + y = 1
-4x + y = -1

becomes

-2x + y - (-4x+y) = 1- (-1)
2x = 2

Answer 12

solve this for x

Answer 13

then sub this value into either

-2x + y = 1 OR -4x + y = -1

and solve for y


the solution is (x, y)

Answer 14

Okay

Answer 15

what'd you get for x?

Answer 16

I'm confused sorry

Answer 17

can you see how we got from

-2x + y - (-4x+y) = 1- (-1)

to
2x = 2
?

Answer 18

Nope

Answer 19

do you know where -2x + y - (-4x+y) = 1- (-1) came from?

Answer 20

Yeah I know where that was from

Answer 21

well the right hand side

-2x + y - (-4x+y)

becomes

-2x + y + 4x - y

-2x + 4x +y - y

-2x + 4x

2x

Answer 22

and the right hand side

= 1- (-1)
= 1 + 1
= 2

Answer 23

so we have found the difference between the equations to be

2x = x

Answer 24

okay I still don't get how I find x from
-2x + y - (-4x+y) = 1- (-1)
2x = 2

Answer 25

2x = 2

divide both sides of the equation by 2

2x /2 = 2/2
x =

Answer 26

Oh I was confused because I was looking at the whole thing
x= 1

Answer 27

good! you are almost there now,

Answer 28

now sub x= 1 into either one of the original equations

-2x + y = 1 OR -4x + y = -1

and solve for y

Answer 29

(-2x1) + y = 1
-2+ y= 1

Answer 30

that's right ....

Answer 31

y = ???

Answer 32

i think y=3

Answer 33

yes!

Answer 34

so you have found x = 1, y= 3 ie (x, y) = (1, 3)

Answer 35

Cool, I missed out on class today but I still had homework. So I needed a little help

Answer 36

if you plug in these values into
the original equations

-2x + y = 1 OR -4x + y = -1

you'll get

-2(1) + 3 = 1 OR -4(1) +3 = -1
-2 + 3 = 1 OR -4 +3 = -1
1 = 1 OR -1 = -1

which are both always true

so you know your solution is correct

Answer 37

Okay

Answer 38

do you have another one like this?

Answer 39

I have a couple

Answer 40

But now I don't have time to solve more.

Answer 41

we found the difference of the equation for this one because it made the y's cancel out ,


sometime you have to add the equations, or something more complex

Answer 42

Okay. Thank you sooo much. I have to leave. I'll post another question if I have problems

Answer 43

ok \[\ddot\smile\]