solve by elimination
0.3x-0.2y=4
0.4x+0.3y=-1

- anonymous

solve by elimination
0.3x-0.2y=4
0.4x+0.3y=-1

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- amistre64

muliply by 10 to get rid of the decimals... that will make it look less intimidating

- amistre64

3x-2y = 40
4x +3y = -10

- yuki

if you multiply 40 on the first eqn
and 30 on the second, you can see which ones can be eliminated

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## More answers

- yuki

your idea is to make the coefficients of either x or y to be equal

- yuki

for most elimination problems, that will work

- amistre64

to eliminate the x variables; *4 the top and *3 the bottom...then subtract

- amistre64

12x -8y = 160
12x +9y = -30

- amistre64

we could combine these steps by mulitply one equation by a negative instead...
12x -8y = 160
-12x -9y = 30
---------------
-17y = 190
y = -190/17

- anonymous

you lost me

- amistre64

where?

- anonymous

12x-8y=160
12x-9y=-30
how did you get those

- amistre64

by subtraction......
12x -8y = 160 12x -8y = 160
-(12x +9y = -30) means -12x -9y = 30
---------------- ----------------

- amistre64

tell me: does this equal out?
5 5
-(-4) +4
---- ---- ???

- anonymous

yes

- amistre64

thats all i did..... just with more numbers involved

- anonymous

how did you get the 12x -8y = 160 & -(12x +9y = -30)

- amistre64

elimination means 'get rid of something'...right?
the only way to get rid of something; to eliminate it; is to get it to zero... otherwise there is something still there right?

- anonymous

right

- amistre64

you are given 2 equations and are asked to eliminate something.... that would either be the xs or the ys right? I choose the xs cause they were in front.

- anonymous

ok

- amistre64

do you recall that in an equation..whatever you do to one side has to be done to the other to keep it equal?

- anonymous

yes

- amistre64

5+3 = 8 when we multiply this by 4 is it still equal?
4(5+3 = 8)..... 20 + 12 = 32 ???

- anonymous

right

- amistre64

do the variables make a difference to it?
4(5x + 3y = 4)......20x +12y = 16...still equal??

- amistre64

we are not changing the 'value'...just the form, its shape, the way it looks..... the value remains the same. right?

- anonymous

right

- amistre64

so lets use this to our advantage..
we want some part of your equation to cancel each other out...
what wer ethe equations again?

- amistre64

0.3x-0.2y=4
0.4x+0.3y=-1
we can multiply both equation by 10 to get rid of the decimal and make it easier to look at right? we change the shape; but not the value

- anonymous

k

- amistre64

3x - 2y = 40
4x +3y = -10 we good here?

- anonymous

yes

- amistre64

we have no terms that are the same...so we have to modify some more..... to get rid of one of them.....or rather a set of them.

- amistre64

if we pick 'x'...what value do 4x and 3x have in common?

- anonymous

x?

- amistre64

x is not a 'value' :) 4x and 3x..... do they have 12x in common? 8x? 29x?

- amistre64

x is a valued pick; but that makes things messier lol

- amistre64

valid pick is what its spose to say...

- amistre64

4x(3) = 12x
3x(4) = 12x.....right?

- anonymous

right

- amistre64

so the top can be *4; and the bottom *3
4(3x - 2y = 40) 12x -8x =160
3(4x +3y = -10) 12x +9y = -30
havent changed anything but the way they look correct?

- anonymous

correct

- amistre64

but if we add these together...nothing is eliminated is it?... what do we have to do to get an elimination now?

- anonymous

wouldnt x be eliminated

- amistre64

how? 12x + 12x = 24x..... that aint zero..

- anonymous

your right i was thinking bout -12x +12x
continue plz

- amistre64

thats right... we need to change the way one of them looks again to get a -12x...
12x -8x =160 12x -8x =160
-1(12x +9y = -30) -12x -9y = 30..now were good to go

- amistre64

can we eliminate now?

- anonymous

yes

- amistre64

we get:
-17y = 190..... solve for y
y = -190/17. right?

- anonymous

yes

- amistre64

since we have a solid value for y...use it to find x

- anonymous

wait how does 190 become -190 and -17 becomes 17

- amistre64

the negative doesnt care what its attached to..... any (+)(-) combonation results in a (-)...right?
does 190/-17 equal something different than -190/17?

- anonymous

i guess not

- amistre64

the proper ettiquiette is to put the sign to the top...

- amistre64

but in some cases its good to know that you can move it around

- amistre64

what wouldve hapened aif we combined steps?

- amistre64

.4(.3x -.2y = 4) .12x -.08y = 1.6
-.3(.4x+.3y =-1) -.12x -.09y = .3
-----------------
-.17y = 1.9
y = -1.9/.17 = -190/17

- anonymous

right

- amistre64

0.4x+0.3y=-1
.4x + .3(-190/17) = -1....solve for x

- anonymous

-5.7

- anonymous

or is it -133/17

- amistre64

4x = -10 + 570/17
4x = (-170 + 570)/17
4x = 400/17
x = 400/4.17 = 100/17

- amistre64

4.17 is a lazy way of writing 4*17

- anonymous

how did yiu get 570/17

- amistre64

i used 3(-190/17) instead of .3(-190/17)
3(-190) = -570
------ ------
17 17
4x - 570/17 = -10
4x = -10 + (570/17)...

- anonymous

oh ok i was doing it by .3

- amistre64

:) .3 was fine, but you would have had to change the decimal eventually

- amistre64

1/.17 cahnges to 100/17

- anonymous

-10*17=-170

- amistre64

.4x + .3(-190/17) = -1
.4x - 57/17 = -1
.4x = -1 + (57/17)
.4x = (-17+57)/17
.4x = 40/17
x = 40/(.4*17)
x = 400/(4*17)
x = 100/17

- anonymous

ok i think i got it

- amistre64

i think i see you trying to get rid of the 17 on the bottom :)

- anonymous

i just dont know how to do this stuff

- anonymous

taking midterms this week these questions are for the practice exam

- amistre64

68x - 570 = -170
68x = -170 + 570
x = 400/68
x = 400/4 100
------- = -----
68/4 17

- amistre64

i got a final grade of 89.06%...and it gave me an 'A' for the course ;)

- amistre64

i dropped 3 writing assignments and still passed with an 'a' lol

- anonymous

thats good!
right now i have a 77.37%

- anonymous

how did you get those answers above 68x....

- amistre64

i times everything by 17 to get rid of the fraction...

- amistre64

4(17) = 68

- anonymous

right but 3(17)=51

- amistre64

3(-190)(17)
---------- = 3(-190)
(17)

- amistre64

17/17 = 1

- anonymous

x=400/68 i divide that by?

- amistre64

thats why its called getting rid of a fraction ;)

- amistre64

400/68 has 4 in common..remember 4(17)? and 4(100) = 400

- amistre64

divide them both by 4

- anonymous

ok now that way makes sense to me

- amistre64

you seem to see numbers and math is a solid concrete building that cant be moved or messes with.
but its really more like silly putty...bend it to your will :)

- amistre64

algebra has 5 rules: and only 5 rules...

- anonymous

whats that?

- amistre64

1. numbers can be moved around (commutative)
2. numbers canbe grouped in different ways (associative)
3. every number has an evil twin (inverse).
4. there is one number that changes nothing (identity)
5. distribute numbers thru paranthesis (distributive)

- anonymous

i will have to make a note of those

- amistre64

3 and 4 are split in 2 by some people to get an additivie inverse/multiplicative inverse and an additive indentity/multiplicative identity

- amistre64

tell me; the 1st rule says we can move number around...
4-5 is the same as -5+4 right?

- anonymous

yes =-1

- amistre64

-10 + 6 is the same as 6 - 10 right?
when you move numbers...pack their luggage, there signs :)

- amistre64

does grouping matter?
3*(4*5) is the same as (3*4)*5 right?

- anonymous

same

- amistre64

3+(5-6) the same as (3+5)-6?
but you gotta keep an eye out for this sometimes....

- amistre64

3-5-6
^ never split a negative/subtractionwith a parenthesis

- amistre64

3+(-5-6) is the same as (3-5)-6

- amistre64

subtraction and division are make believe..... there is only addition and multiplication that is real.

- anonymous

yes=-8

- amistre64

3-5 means 3+-5

- amistre64

5-2 means 5+ -2

- amistre64

the evil twin rule.... accounts for subtraction and division...

- amistre64

what is the evil twin of 15? its -15
the evil twin of -3 .... is 3

- amistre64

the evil twin of 6, when multiplying is 1/6 tho..... thats why some people split the rules

- anonymous

thought it was -6

- amistre64

additions evil twin is the opposite of a number; -9 ; 9
multiplications evil twin is the upside down; 8 ; 1/8

- amistre64

recpirocal is an upside down fraction rigt?
the evil multplication twin of 3/4 is 4/3
the evil addition twin of 3/4 is -3/4

- amistre64

the evil addition twin of 18 is -18
teh evil multiplication twin of 18 is 1/18

- amistre64

what is the addition identity number?
4 + ? = 4
-9 + ? = -9
17 - ? = 17

- amistre64

what is the multiplcation identnty number?
6*? = 6
14*? = 14
(-5/8)*(?) = -5/8

- amistre64

when evil twins meet; they form the identity number:
4+ -4 = 0
12 + -12 = 0
-7 + 7 = 0
4(1/4) = 1
2/5(5/2) = 1
(129/17) (17/129) = 1

- amistre64

and rule 5; distribution
5(3+6) = 45
5(3) + 5(6) = 45
15 + 30 = 45
45 = 45

- amistre64

whatever we can distribute together; we can undistribute as well...which is what we cal factoring quadratic equations

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