Question

I'm having a terrible time with solving linear equations by the addition/elimination method. Here is my problem: 3x+9y=12, 5x-4y=3. Can anyone help?

Answer 1

i assume that 5x+4y?

Answer 2

or 5x-4y :p

Answer 3

no, these are the equations given in the question. I'm really lost now.

Answer 4

multiply or divide to get the same "value" of a term, but opposites, in each equation

Answer 5

these are the exact equations? no typos???

3x+9y=12
and
5x=4y=3

Answer 6

3x+9y=12, 5x-4y=3

Answer 7

LOL

Answer 8

divide the top by 3 and the bottom by -5

Answer 9

x+3y =4
-x+4y/5= -3/5

then add together and solve for y

Answer 10

instead of dividing,wouldn't multiplying by 4 and 9 be easy??then add..

Answer 11

define "easy" ;)

Answer 12

not involving fractions here...

Answer 13

x+3y =4
-x+4y/5= -3/5
---------------
19y/5 = 17/5
y = 17/19

Answer 14

not sure why "not involving fractions" makes it easier ... unless you fear pie ;)

Answer 15

OK-now I'm totally lost. This is what I'm doing: 3x+9y=12
5x-4y=3
I combine these two equations to equal 8x+5y=15 IS THIS RIGHT?

Answer 16

lol! :P i thought 12-45 would be easier for her than 3+4/5....

Answer 17

no, you have not eliminated any of the variables by that process

Answer 18

I mean for a starting equation, I realize I have to solve for the variables

Answer 19

you havent created a situation where one of the variables is removed; all you have done is create a line that has an infinite number of solutions

Answer 20

OK, then can you explain the steps? Please go slow, and try not to laugh. I'm 55 taking Algebra for the 4th time and I'm determined to get this stuff.

Answer 21

elimination, by its namesake alone, eliminates one of the variables in the process so that we are left with a single variable to play with.

does that make sense?

Answer 22

yes

Answer 23

does it make sense that we can scale an equation and it still retains its inherent solutions; that only the form of it is altered?

Answer 24

scale?

Answer 25

to scale means: to multiply or divide by a constant

Answer 26

you can't solve any equation unless it has only one variable

Answer 27

vikrant, thats not quite accurate.

Answer 28

Then we can "scale" an equation and still retain the solution. Only the form is altered. Is that right?

Answer 29

if you multiply an equation with any number... it doesn't effects... just try to make coefficients of any one variable equal.

Answer 30

P.S-My English is poor

Answer 31

I dont understand what you are saying

Answer 32

correct

so we want to scale the given equations so that we can eliminate one of the variables and only focus on a single variable

Answer 33

OK

Answer 34

for example

y = x is a line equation

if we scale this by 2 we get:
2y = 2x which has the same solutions as y=x

if we scale this by -4 we get:
-4y = -4x which has the same solutions as y=x

if we scale this by any constant "c" we get:
cy = cx which has the same solutions as y=x

Answer 35

^^YAy!!

Answer 36

got it

Answer 37

so, lets look at your system of equations, and see what we can scale them by to help us eliminate one of the variables in the process

Answer 38

ok

Answer 39

This is always where I get stuck.

Answer 40

im going to focus on eliminating the x parts

3x+9y=12
5x-4y=3

if we had x up top and -x on the bottom; then x-x=0

correct?

Answer 41

correct

Answer 42

so, 3x/3 = x
5x/-5 = -x

so my simplest idea is to scale the top by 1/3 and the bottom by -1/5

Answer 43

I don't understand where you got -5 from

Answer 44

nevermind

Answer 45

\[\frac{3x+9y=12}{3}\]\[\frac{5x-4y=3}{-5}\]

\[x+3y=4\]\[-x+\frac{4}{5}y=-\frac35\]

Answer 46

WHEW! I'm going to try and digest this now. I think with your help on this problem, I will be able to do more problems like it.

Answer 47

keep in mind that we can scale these by ANY constant factor; so
we did not have to use 1/3 and -1/5; those were just what I chose for convience to me

Answer 48

so I can use ANY numbers?

Answer 49

yes; but in the end you desire a situation where you can eliminate one of the variable

Answer 50

So how did you come up with 1/3 and -1/5?

Answer 51

because they make coefficients of x in both equations same..

Answer 52

i wanted the situation where: x + (- x) = 0

(3x) + (5x) = 0

this tells me that i would want to divide the top by 3 and the bottom by -5

Answer 53

ok-I think my light bulb is beginning to glow. You have been a great deal of help to me and I appreciate it beyond words. God Bless You for helping a poor old grandma get through this!

Answer 54

we can use the same concept; and instead of the situation: x + (-x) = 0, we might think it easier to have 15x + (-15x) = 0

(3x) + (5x) = 0

then we could multiply the top by 5 and the bottom by -3, right?

5(3x) + (-3)(5x) = 0

Answer 55

got to think on this...

Answer 56

good luck with it ;)

Answer 57

You are so very kind, I see the 15x +(-15x) = 0 now. I will continue to work on this, thanks again, you are my hero today! Deb

Answer 58

Here is an example being worked out
http://www.khanacademy.org/math/algebra/systems-of-eq-and-ineq/v/addition-elimination-method-2