Question

Solve by ELIMATION.
2x-3y=61
2x+y=-7

Answer 1

Multiply everything in equation 2 by -1 to go from

2x+y=-7

to

-2x-y=7

Answer 2

So you'll have this new system

2x-3y=61
-2x-y=7

Now add the equations to get

2x-3y=61
-2x-y=7
----------
0x - 4y = 68

so this means

-4y = 68

y = ???

Answer 3

y=-17

Answer 4

good

Answer 5

now use this to find x

Answer 6

pick any equation with x and y, plug in y = -17 and solve for x

2x-3y=61

2x-3(-17)=61

2x + 51 = 61

...
...
...

x = ???

Answer 7

x=-5

Answer 8

no

Answer 9

I meant positive 5. What about this problem: 2x+18y=-9 & 4x+18y= -27

Answer 10

good, x = 5, y = -17

Answer 11

notice how we have 18y in each equation

Answer 12

if we add them we get 18y + 18y = 36y which isn't 0y

but if we change the sign of either 18y, we will be able to add them so we get 0 since 18y + (-18y) = 0y = 0

Answer 13

see how this works?

Answer 14

So would we multiply it by -1?

Answer 15

yes, either equation (both sides of it)

Answer 16

Would x equal 9?

Answer 17

no

Answer 18

What would it be then?

Answer 19

if you multiplied both sides of equation two by -1, then you would have

2x+18y=-9
-4x-18y= 27

Answer 20

adding the equations gives you

2x+18y=-9
-4x-18y= 27
------------
-2x + 0y = 18


so, -2x = 18 ----> x = ??

Answer 21

Okay I have that.

Answer 22

but x is not 9

Answer 23

since

-2x = 18

-2(9) = 18

-18 = 18

is not true

Answer 24

so what is x instead?

Answer 25

I don't get it..

Answer 26

-2x = 18

divide both sides by -2 to isolate x

x = 18/(-2)

x = -9

Answer 27

so you were close, just off by a sign

Answer 28

now use this to find y

Answer 29

I even had that haha I just didn't see the sign

Answer 30

oh lol, that's good

Answer 31

anyways, what do you get for y?

Answer 32

y=1/2

Answer 33

good

Answer 34

Okay next one, 3x-10y=-25 & 4x+40y=20

Answer 35

are any of the x or y coefficients equal? or equal and opposite in sign?

Answer 36

Negative 10 and positive 40 are opposites in signs

Answer 37

how can you change the -10y to -40y ?

Answer 38

so you can add -40y and +40y to get 0y

Answer 39

Multiply -10 by positive 4

Answer 40

good

Answer 41

you have to do that to both sides of everything you change in the equation that has -10y

Answer 42

so multiply both sides of 3x-10y=-25 by 4 to get

3x-10y=-25

4(3x-10y)=4(-25)

12x - 40y = -100

Answer 43

So

3x-10y=-25
4x+40y=20

turns into

12x - 40y = -100
4x+40y=20

Answer 44

Okay would you add or subtract?

Answer 45

add because -40y + 40y = 0y

Answer 46

okay would x=-5?

Answer 47

that is correct

Answer 48

And y=1

Answer 49

good

Answer 50

Okay two more left. x-8y-18 & -16x+16y=-8

Answer 51

Would you multiply the first one by -2

Answer 52

x-8y-18 looks like a typo

Answer 53

I meant =18

Answer 54

ok so x-8y=18

Answer 55

if you multiply both sides by 2, you get 2x-16y = 36

Answer 56

x-8y=18
-16x+16y=-8

turns into

2x-16y = 36
-16x+16y=-8

Answer 57

I thought it would -2x-16y=36

Answer 58

why -2x ?

Answer 59

And wouldnt the 36 be negative too

Answer 60

18 is positive, so multiplying +2 by +18 gives you +36

Answer 61

I thought we were multiplyinh it by -2 sorry.

Answer 62

oh i see, no we're using +2

Answer 63

if we used -2, then -8y would turn into 16y

Answer 64

we want it to be -16y so the -16y and +16y add to 0y

Answer 65

the terms have to have equal coefficients but opposite signs so they add to 0

Answer 66

It would be x=-2

Answer 67

x = -2 is correct

Answer 68

Any y= -2 1/2

Answer 69

or y = -5/2, nice work

Answer 70

Would 88x-5y=39 & -8x+3y=-1 be 0,7 4/5

Answer 71

no assuming there are no typos in the original equations

Answer 72

Will you walk me through it?

Answer 73

we have 88x and -8x

what can we do to -8x to get it to -88x?

Answer 74

Multiply it by 11

Answer 75

so you have to multiply both sides of equation 2 by 11

Answer 76

that means


88x-5y=39
-8x+3y=-1


turns into


88x-5y=39
-88x+33y=-11


Add the equations to get:


88x-5y=39
-88x+33y=-11
------------
0x + 28y = 28


which means 28y = 28


so what is the value of y?

Answer 77

y=1

Answer 78

use that to find x

Answer 79

x=1/2

Answer 80

perfect

Answer 81

Thank you so much for your help! I really appreciate it!

Answer 82

sure thing