Question

Solve each system using elimination.
3x+3y=27
x-3y=-11

9. 2x+4y=22
2x-2y=-8

11. 5x-y=0
3x+y=24
Please show your work!! Thank you!!

Answer 1

first one add the y's and solve for x.. then plug back the x to find the y

Answer 2

3x + 3y = 27
x - 3y = -11

3y cancels out

3x + x = 27 + -11
4x = 16
there x = 4.

Sub that into equation (2).... x -3y = -11

4- 3y = -11

-3y = -15

there fore y = 5.

x =4, y =5

Answer 3

Thank you soo much @BizPro
Can you help me with the others??

Answer 4

@ganeshie8
@satellite73
@jim_thompson5910
@Zarkon
Please help!!

Answer 5

I need help with the last two problems, 9 and 11

Answer 6

for #9, my hint is to multiply everything in equation 2 by 2 to go from this

2x-2y=-8

to this

4x-4y=-16

------------------------

we now have this system

2x+4y=22
4x-4y=-16


notice how we haev +4y in the top and -4y in the bottom. They add to 0y, aka 0, and go away and the y terms are eliminated when you add the equations of this new system

2x+4y=22
4x-4y=-16
----------
6x + 0y = 6


So 6x = 6 ----> x = ????

Answer 7

x=1?

Answer 8

Good, now take that value of x and plug it into any equation that has x and y in it.

From there solve for y

Answer 9

For instance,

2x+4y=22

2*1+4y=22 ... plug in x = 1

2 + 4y = 22

...
...
...

y = ???

Answer 10

Does y=-4??

Answer 11

no

Answer 12

try it again

Answer 13

I am confused..

Answer 14

2 + 4y = 22

4y = 22 - 2

4y = 20

y = ???

Answer 15

In the first equation..2x+4y=22 we got that x=1.
Not to figure out why, I must plug in x into 2x-2y=-8, right?
I plugged it into that equation and my answer came out to be y=-4

Answer 16

2x-2y=-8

2(1)-2y=-8

2 - 2y = -8

-2y = -8 - 2

-2y = -10

y = ???

Answer 17

No matter which equation you pick, you should get the same answer for y.

Answer 18

-5

Answer 19

closer, but no

Answer 20

-2y = -10

y = -10/(-2)

y = 5 ... it's positive since the negatives cancel

Answer 21

4y = 20

y = 20/4

y = 5 ... same answer

Answer 22

Okay, can you please help me with the next question?

Answer 23

Add the equations to get


5x-y=0 ... notice how the y terms are equal yet opposite
3x+y=24 ... notice how the y terms are equal yet opposite
---------
8x + 0y = 24


8x = 24 ----> x = ???

Answer 24

x=3

Answer 25

Now use that to find y

Answer 26

Am I doing this right?
3(3)+y=24
9+y=24
9y=24

Answer 27

9+y does NOT turn into 9y

Answer 28

9y means "9 times y" and it's completely different from 9+y

Answer 29

Okay...So then how would I do it? I am lost right now.

Answer 30

hint: 9+y is the same as y + 9

Answer 31

so

9+y=24

is the same as

y + 9 = 24

Answer 32

oh..do I switch around the equation? y=24+9?

Answer 33

no, you need to move that +9 over

Answer 34

so what must you do to both sides?

Answer 35

divide or subject?

Answer 36

which operation undoes addition?

Answer 37

subtract, sorry. I mixed up the word with subject

Answer 38

it's ok

Answer 39

which operation undoes addition?

Answer 40

now Y equals 24-9

Answer 41

y=15

Answer 42

good

Answer 43

wow! Thank you soo much for your help! Can you help me with a few more?

Answer 44

I can help with one more

Answer 45

Okay. 12x+2y=90
6x+2y=60

Answer 46

notice if you add the equations, the y terms will be 2y+2y = 4y, which is NOT 0y or 0 like we want.

We can fix this by changing the signs of each term in either equation. So change the signs of each term in the second equation to get -6x - 2y = -60. Now add the equations


12x + 2y = 90
-6x - 2y = -60
--------------
6x + 0y = 30

Notice how the y terms are gone now leaving us with

6x = 30

x = ??

Answer 47

x=5

Answer 48

Now use it to find y

Answer 49

y=15

Answer 50

good

Answer 51

I have 3 more of the equations left, can I work them through and you just watch to make sure I am doing them right?

Answer 52

Sure I can do that. Go ahead

Answer 53

Thanks. Okay, the first one is 2x+3y=9
x+5y=8

Answer 54

2x+3y=9
x +5y=8
_________
2x+8y=17
Is that right so far?

Answer 55

well first off, 2x + x is 3x (not 2x)

and notice how 3y + 5y = 8y which is not 0y or 0

We want either the x or y terms to be eliminated. This doesn't happen here.

Answer 56

What can you do to fix this?

Answer 57

Okay, let me try again.
2x+3y=9
x -5y=8
_________
3x+0y=17
Now is that right?

Answer 58

now 3y + (-5y) = -2y which is still not 0y

Answer 59

also, you need to do the same thing for all terms in the second equation (you cannot just change the sign of one term)

Answer 60

I don't know what to do now.

Answer 61

we have 2x in the top equation and an 'x' in the bottom equation

why not multiply that x in the bottom equation by -2 to get -2x

now notice how 2x + (-2x) = 2x - 2x = 0x = 0

Answer 62

So what you have to do is multiply everything in equation 2 by -2 to get

x+5y=8

-2*x + (-2)(5y) = -2*8

-2x - 10y = -16

Answer 63

This means the system

2x + 3y = 9
x +5y = 8

turns into

2x + 3y = 9
-2x - 10y = -16

Answer 64

And now do I subtract?

Answer 65

add the equations actually

Answer 66

since 2x + (-2x) = 0x

Answer 67

so it would be -4x-13y=-25?

Answer 68

you're adding the equations incorrectly (see my last post)

Answer 69

x+13y=-25?

Answer 70

2 + (-2) is the same as 2 - 2

Answer 71

I am lost again.

Answer 72

2x + (-2x) is the same as 2x - 2x

Answer 73

I understand that, so then why is 0x-13y=-25 wrong?

Answer 74

3y + (-10y) is not -13y

Answer 75

9 + (-16) is not -25

Answer 76

0x=-7y=-7?

Answer 77

closer, but it should be

0x + (-7y) = -7

which is I'm sure what you meant to say

Answer 78

so...

0x - 7y = -7

-7y = -7

y = ???

Answer 79

y=1

Answer 80

Now x=3

Answer 81

perfect on both

Answer 82

Okay, can I try another one?

Answer 83

6x+4y=42
-3x+3y=-6

6x+4y=42
-3x+3y=-6
_____________
3x+7y=26

Does that look right?

Answer 84

were any variables eliminated?

Answer 85

No..so do I subtract instead?

Answer 86

hint: look at the x terms and try to eliminate them

Answer 87

is x=5

Answer 88

Do you see how to get x = 5?

Answer 89

well it had -9x=-48..I divided it.

Answer 90

-9x = -48 doesn't lead you to x = 5

Answer 91

Is it wrong?

Answer 92

add 6x and -3x to get 3x

That is NOT 0x

how can we change that -3x into something that adds to 6x to get 0x?

Answer 93

multiply it

Answer 94

by what

Answer 95

2

Answer 96

so it would be -6x+6y=-12

Answer 97

y=3