Question

-4x+4y=-7
5x-6y=7
I cant eliminate here,right? So what do i do?

Answer 1

What do you mean?

Answer 2

First multiply each of the equations by a different factor to let either the x coefficients or y coefficients be the same. Them just add the two so the one variable would be cancelled out.

Answer 3

You can eliminate them as slaaibak said. think lowest common multiple between the coefficients of one of the variables.

Answer 4

Oh i see, so i could do this?
-4x+4y=-7-------------12x+12y=-21
5x-6y=7--------------10x-12y=14 To cancel out the 12s?

Answer 5

bingo

Answer 6

So i would have -12x+12y=-21 + 10x-12y=14 = -2x=7?

Answer 7

yep

Answer 8

-2x=-7

Answer 9

sorry, -7
careful
oh you caught it

Answer 10

-2x=-7 =-7/2?

Answer 11

yep yep!
and now for y...

Answer 12

no, sorry positive again

Answer 13

negative over negative...

Answer 14

Substitute 5x-6y=7 getting 5*7/2-6y=7

Answer 15

Oh right

Answer 16

you caught it anyway
so far so good, you're doing better than me this morning lol

Answer 17

35/10-6y=7?

Answer 18

Lol xd

Answer 19

where did the ten come from?

Answer 20

Oh, so i dont multiply 5 by both parts of the factor?
35/2-6y=7?

Answer 21

much better :)

Answer 22

in general we have this situation:\[c*\frac{a}{b}=\frac{c}{1}*\frac{a}{b}=\frac{ca}{b}\]so when a number is alone we always treat it as over one...

Answer 23

Ohhhh, now i get it!

Answer 24

try to relate it to those rules for algebra
so what is y?

Answer 25

35/2-6y=7
Im not really sure what to do here, maybe make the two sides factors match.
35/2-6y=14/2?

Answer 26

that's a good start
now get y on one side and the constants on another

Answer 27

35/2-6y=14/2
-6y=-21/2

Answer 28

Good so far?

Answer 29

yes :)

Answer 30

-6y=-21/2
-y=-(21/2)/6

Answer 31

No that cant be it

Answer 32

I need to make the factor divisible by six

Answer 33

first off take the -1 with the 6, we don't want y to be negative..
second it is right, but you need to simplify it
remember that dividing by a number is the same as multiplying by it's inverse

Answer 34

That would mean that i have to divide both sides by -6, right?

Answer 35

right, and what is (-21/2)/(-6) ???
do you know the trick fro this?

Answer 36

y=-42/4 / -6? y=7/4

Answer 37

yes!!!
dang you learned a lot Inopeki, nice :D
many people here hate systems, it'll be nice to have you help them :P

Answer 38

:D Yes!!

Answer 39

that's very impressive doing systems like that, I can honestly say I'm impressed. Again, awesome :D

Answer 40

Thanks :D

Answer 41

Give me another one :D

Answer 42

well, systems can be tricky to make up off the top of your head. If you're not careful they can get messy...

Answer 43

ok here's one...
x-2y=4
3x+6y=3
I think this is a bit easier than the last...

Answer 44

im sorry, OS crashed

Answer 45

I'm in no rush, don't worry

Answer 46

x-2y=4-----------3x-6y=12
3x+6y=3----------3x+6y=3

Answer 47

pellet

Answer 48

They will cancel out, i cant do that

Answer 49

no wait

Answer 50

3x-6y=12 + 3x+6y=3 = 6x=15
15/6=x?

Answer 51

yep, just simplify the fraction

Answer 52

5/2?

Answer 53

sweet :)
and for y...?

Answer 54

5/2-2y=8/2
-2y=13/2?

Answer 55

watch the signs... made a little mistake

Answer 56

Ah, -2y=3/2?

Answer 57

there ya go !

Answer 58

-2y=3/2
y=6/4 / -2
y=-3/4?

Answer 59

very nice!
do you know how to check your answers?

Answer 60

Yeah, put the final answers in to one of the equations to see if it is true.
5/2-2*3/4=4

Answer 61

Now that just doesnt make sense with fractions...

Answer 62

you should really put it in both equations, but yes you got the idea

Answer 63

it is correct:
5/2-2(-3/4)=5/2+3/2=8/2=4
again, you dropped a negative for the y-value. That happens to me a lot in systems too, just gotta be careful

Answer 64

try to verify that the other equation is true

Answer 65

The first one in this question?

Answer 66

the other equation in the system:
3x+6y=3

Answer 67

Oh

Answer 68

3*5/2+6*-3/4=3
15/2- -18/4=3
15/2- -9/2=6/2?

Answer 69

=3

Answer 70

so it must be right :)
nicely done

Answer 71

Thanks :D Now what?

Answer 72

you should always check both equations, I'm not sure who told you that checking just one is okay, it's really not.
Watch:
x-2y=4
3x+6y=3
no what if I got the answer x=6, y=1
the first equation would give
6-2(1)=4 True
but the second...
3(6)+6(1)=3 False
so you must check both
each equation by itself has infinite solutions, you need to use the other equation to just get one.

Answer 73

now what if*

Answer 74

Oh, now i see why.

Answer 75

because if we solve say the first one for x...
x=2y+4
we have a function again:
y=1
x=2(1)+4=6
y=2
x=2(2)+4=8
etc...

next? I guess systems with 2 unknowns when you're comfortable with this stuff.
What else are you doing? quadratics?

Answer 76

After this, its an introduction to ratios

Answer 77

Oh you mean what i HAVE been doing?

Answer 78

I meant the next step would be with 3 unknowns, you already are doing 2...
but yeah, let's practice things you have just learned recently

Answer 79

I leanred averages,taking procent, slope, y-intercept,graphing lines, graphing points, integer sums.

Answer 80

equation of a line, equation systems

Answer 81

lol that's a lot...
what do you mean by integer sums?

Answer 82

Like if the sum of 5 odd consecutive integers is 217, what is the largest odd integer?

Answer 83

Actually thats 7 odd consecutive integers.

Answer 84

nice
those are fun... well for a lot of us at least.
what do you feel unsure about? let's work on that
but I need to get breakfast...

Answer 85

Yeah, i need to get something to eat too

Answer 86

ok we'll regroup in 10-15

Answer 87

Sure

Answer 88

Why does it say that im level 23?

Answer 89

ok I'm back
now what to work on...
let's see how you are with distribution real quick:
simplify
2x(3+4x-2/x)

Answer 90

2x(3+4x-2/x)
2(3+4x-2)
2(1+4x)

Answer 91

careful, that 3 is lonely...

Answer 92

What?

Answer 93

and x(4x) is not 4x

Answer 94

wait!

Answer 95

middle step
...

Answer 96

2x^2(3-2)?

Answer 97

not quite. Middle step:
2x(3+4x-2/x)=2x(3)+2x(4x)-2x(2/x)=???
^^^^^very important step for you, you'll see why when you do factoring

Answer 98

Oh right!