Question

HELP! WILL MEDAL AND FAN!!

Solve the following system of equations:

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

Answer 1

Add the 1st equation to the negative of the 2nd equation.

What do you get?

Answer 2

Y= -2x + 1
and
Y= -4x - 1

Answer 3

Y= -2x + 1
and
Y= -4x - 1

Answer 4

Like this

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

Do you see what happened here?

Answer 5

yeah

Answer 6

So what do you think we should do with that last equation?

Answer 7

solve it or simplify it

Answer 8

Ok, try it out - I'll watch and help

Answer 9

are you tring to put it into y= form?

Answer 10

How can we simplify this -
-2x -(-4x) + y - y = 1 -(-1)
?

Answer 11

-2x+y=1

Answer 12

See the y - y will cancel to become zero
$$
-2x -(-4x) + 0 = 1 -(-1)\\
$$
What's else can we do?

Answer 13

subtract the values and get -6x

Answer 14

Close

The -(-4x) becomes just 4x:
$$
-2x +4x + 0 = 1 -(-1)\\
$$
Now what?

Answer 15

What is -2x + 4x ?

Answer 16

2x

Answer 17

yes!
So now we have
$$
2x+0=1-(-1)
$$
What's can we do next?

Answer 18

2x+0=-2

Answer 19

-(-1) = 1

Remember, negative of a negative number makes it positive

Try again

Answer 20

2x+0=1

Answer 21

$$
2x+0=1-(-1)=1+1
$$
Do you see that?
What's next?

Answer 22

2x+0=2

Answer 23

yes!
Ok, what do we do now?

Answer 24

subtract 0 from both sides and get

2x=2

Answer 25

What next?

Answer 26

the answer choices are

A. (3,1)
B (-1,3)
C (-1,-3)
D (1,3)

Answer 27

We need x by itself, what do we need to divide out on both sides to make 2x equal to just x ?

Answer 28

2 divided by both sides

Answer 29

Yes!

We need to divide 2 to both sides:
$$
\cfrac{2x}{2}=\cfrac{2}{2}=?
$$
What does this give us for x?

Answer 30

x=0

Answer 31

x=1

Answer 32

Yes!
Now you know one variable.

Now let's use one of your original equations to get y
Let's use this one
$$
-2x + y = 1
$$
Plug in x=1 and see what you get for y.

Answer 33

$$
-2\times 1 + y = 1
$$
So now what is y?

Answer 34

-2y=1

Answer 35

$$
-2\times 1 + y = -2+y=1
$$
See that?

Answer 36

yeah

Answer 37

How do you move the -2 to the other side of the equal sign?

Answer 38

im so confused this isnt leading to any of the answer choices

Answer 39

and i have so many more questions in so little time

Answer 40

Add 2 to both sides of this equation
$$
-2+y+2=1+2
$$
What does this give us?

Answer 41

-2 + 2y = 3

Answer 42

Almost there
$$
-2+2+y=3
$$

Answer 43

What's -2 + 2?

Answer 44

0

Answer 45

y=3

Answer 46

Yes!

So now you know everything.

x=1
y=3
(1,3)

Answer 47

oh thats make so much sense thanks so much

Answer 48

When you do one on your own, all the others will be like adding 1+1=2

Answer 49

do another on your own
right here

Answer 50

Have some courage my friend, everything takes time -- don't worry about the little things.