Question

Solve the following system of equations:
1/2 x + 1/3y = 7
1/4x + 2/3y = 6

how do I solve it?

Answer 1

Multiple choices:
1. (1/6,14)
2. (6,12)
3. (10 2/3,5)
4. (2 4/9, -1/6)

Answer 2

Are the fractions confusing you? If so, just multiply the first equation by 6 and the second by 12.
3x + 2y = 42
3x + 8y = 72
Can you solve now?

Answer 3

not really, what exactly am i suppose to multiply to get the answer?

Answer 4

It's rather a process that just one step. Multiply the first equation by -1. Then add vertically combining like terms.
-3x - 2y = -42
3x + 8y = 72
The x values cancel.
6y = 30
Solve for x here and plug hat in for y here and solve for x:
3x + 2y = 42

Answer 5

I am sorry but i am so bad at math, I still have no idea what you're talking about...

Answer 6

and how to do it

Answer 7

Alright. THere are several methods for this, but the most basic which you probably should eb using are elimination, graphing and substitution. Here are a few links. The first is elimination and the second is substitution. The graphing part can be done by graphing the lines and seeing where they cross.
http://www.purplemath.com/modules/systlin5.htm
http://www.purplemath.com/modules/systlin4.htm

Answer 8

If you still have questions, you can ask me here.

Answer 9

3/4 + 0.9 =13?

Answer 10

First of all, when you add them, it should be 3/4x + y = 13 because 1/3 + 2/3 = 1.
Second, the purpose of elimination is to get one of the terms to cancel so that you can solve for a variable. If you have 3/4x + y = 13, then you can't solve for x or y can you since you don't know either value.

Answer 11

If you go farther down the link, it'll show you what to do for that kind of thing.

Answer 12

For the frist part in the first sentence, it should be 1/3x + 2/3y = 13

Answer 13

wow, so confusing but okay so I got that the first equation is changed to 1/3x + 2/3y = 13

Answer 14

Double mistake. When I put: First of all, when you add them, it should be 3/4x + y = 13 because 1/3 + 2/3 = 1.
The "1/3 + 2/3 = 1" should be 3/4x + y = 13

Answer 15

omg... okay, i am dying here ... 3/4x + y = 13 got it

Answer 16

then what do i do next?

Answer 17

I'll show you what I did to solve this using elimination and you can browse what they did for the other examples later.
1/2 x + 1/3y = 7
1/4x + 2/3y = 6

1/2 x + 1/3y = 7
-2(1/4x + 2/3y = 6)

1/2 x + 1/3y = 7
-1/2x - 4/3y = -12
ADD VERTICALLY!
1/2 x + 1/3y = 7
-1/2x - 4/3y = -12
------------------
0 - y = -5

-y = -5
y = 5

Then plug this in for y and solve for x.
1/2x + 1/3y = 7

1/2x + 1/3(5) = 7

1/2x + 5/3 = 7

1/2x = 7 - 5/3

1/2x = 16/3
x = 32/3
which when you put into mixed number form is x = 10 2/3
Then, (10 2/3, 5) is the answer. Do you get it?

Answer 18

why did you use (-2)?

1/2 x + 1/3y = 7
-2(1/4x + 2/3y = 6)

Answer 19

I used -2 because -2(1/4) = -1/2 right? See how if you add 1/2 and -1/2, they turn to 0?

Answer 20

okay, thank you so much for your help and time.. :)

Answer 21

Anytime :)