Question

Write an equivalent equation of 12 - 3x = y

Solve the s ystems of equations using the elimination method.
x + 3 = 7 and 3x +4y = 7

Answer 1

Please show your process if you can :)

Answer 2

No i don't

Answer 3

I know that they equal to eachother and that they are on the same line on a graph.

Answer 4

The first step in learning algebra is to become familiar with its vocabulary.

Equivalent equations are equations that have the same solution set over a given domain.

Answer 5

Solution Set over a given domain?

Answer 6

So to write an equivalent equation of 12 - 3x = y

you just rewrite it in an equivalent form.

Answer 7

Use the idea of balance to solve for x.

Answer 8

Re-writing in equivalent form... Sounds pretty confusing.

Answer 9

How would i start?

Answer 10

$$\Huge 12 - 3x = y$$ $$\Huge 12 - 3x +3x= y+3x$$ $$\Huge 12 = y+3x$$
$$\Huge 12 -y= y+3x-y$$ $$\Huge 12 -y = 3x$$ $$\Huge \frac{1}{3}(12 -y) =\frac{1}{3} 3x$$ $$\Huge 4 -\frac{1}{3}y = x$$

Answer 11

$$\Huge x = 4 - \frac{1}{3}y$$$$\Huge\text{and}$$ $$\Huge y=12 - 3x $$ $$\Huge\text{are equivalent equations.}$$

Answer 12

How did you get from 1/3(12-y) = 1/3 3x to 4-1/3y = x?

Answer 13

the distributive property a(b+c)=ab+ac

Answer 14

How did the 12 become 4 ?

Answer 15

(1/3)(12) = 4

Answer 16

Oh i see.

Answer 17

Do you always have to flip the variables to the opposite sides when rewriting into an equivalent equation?

Answer 18

No, I did it for appearance.

Answer 19

So when writing Equivalent Equations.. lets see if i made one up 4 -4x = y

Would it be like
+4x
4 = y + 4x
-y
4 -y = 4x
(1/4)(4/1)
4 -y = x?

Answer 20

And what about my last question about the elimination method.

Answer 21

Oops, your last step should be multiply both sides by 1/4

Answer 22

MMM isn't that what i did?

Answer 23

1/4)(4/1)
1 x 4 = 4
1 x 4 = 4

Answer 24

oh it should have been 1?

Answer 25

1 -y = x?

Answer 26

4 -y = 4x
(1/4) (1/4)

Answer 27

4 -y = 4x
(1/4)(4-y) = (1/4)4x

Answer 28

Oh we have to do it to the entire side.

Answer 29

1 -1/4y = x?

Answer 30

Yes :-)

Answer 31

Oh i see, thank you very much. :) And how would i solve the system of equations using the elimination method if you don't mind me asking.

Answer 32

any ideas?

Answer 33

MMmi know when you use the elimination method you're supposed to get rid of some variables maybe by using their opposite. But i wouldn't know where to start.

Answer 34

Let's look at x + 3 = 7 and 3x +4y = 7 and decide what is a convenient variable to solve for? We have two choices, right?

Answer 35

Yeah x and y

Answer 36

3 didn't have a variable which confused me.

Answer 37

We would probably solve for x?

Answer 38

yes

Answer 39

which equation do you want to solve for x

Answer 40

x +3 = 7

Answer 41

ok, do it please