Question

The sum of two numbers, x and y, is 12. The difference of x and two times y is 6. What are the values of x and y?

A.) x=8, y=4
B.) x=10, y=2
C.) x=18, y=-6
D.) x=20, y=-8

Please Help

Answer 1

you have to set up a system of equations. "the sum of two numbers is 12" means x + y = 12. "the difference of x and two times y is 6" means x - 2y = 6. so those are our two equations

x + y = 12
x - 2y = 6

there are different ways to solving this kind of problem. i think i'd go with the elimination method...

Answer 2

to do that, i'm going to multiply the whole second equation by -1, changing all the signs in the equation

so -1(x - 2y = 6) is -x + 2y = -6

Answer 3

then i'm going to combine the equations and eventually solve for y

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

3y = 6
y = 2

Answer 4

so the answer is ?

Answer 5

and the only choice with y as 2, is b

Answer 6

thank you so much i have more questions also

Answer 7

i will help you only if you try it out yourself first :)

Answer 8

Consider this system of linear equations:

y − x = -13
-4x + 3y = -51

The solution of the system of equations is

A.) 112/5, 47/5
B.)-12, 1
C.) -12, -1
D.) 12,-1

Answer 9

Y - x = -13

Answer 10

do you have any ideas?

Answer 11

none at all like im very horrible at math i do not understand any of this what so ever

Answer 12

ok, so for the sake of teaching, i'm going to use a different method this time; the substitution method...

Answer 13

y - x = -13
-4x + 3y = -51

first, i'm going to use the first equation to solve for y.
once i add x to both sides, y = -13 + x.

now that i know what y equals in terms of x, i'm going to substitute that into the second equation.

-4x + 3y = -51
-4x + 3(-13 + x) = -51

distribute the 3
-4x - 39 + 3x = -51

combine like terms
-x - 39 = -51

add 39 to both sides
-x = -12

divide both sides by -1 to make -x positive
x = 12

and there's no reason to do any further math, because the only choice with x as 12 is d

Answer 14

so the answer is D?

Answer 15

yes

Answer 16

and if you have any more questions, i'm not going to do everything for you next time

Answer 17

are you understanding what i'm doing?

Answer 18

no not at all like math is so hard i dont understand math at all its the hardest subject ive ever taken ive already failed algebra 1 once now im just doing credit recovery so i can get into my right grade which is 11th

Answer 19

do you have any questions about what i did to get the answer?

Answer 20

asking questions about stuff you don't understand is a key element to learning

Answer 21

if you don't ask questions, how could i possibly know what you don't understand?

Answer 22

umm not really cause if you explained it i wouldnt get it

Answer 23

its just the WHOLE algebra 1 subject i dont understand anything

Answer 24

regarding this problem, what don't you get? i explained every step. does my explanation help at all?

Answer 25

not really because i dont understand it

Answer 26

my goal right now is to help you understand. look back to my explanation and tell me any terms you don't know

Answer 27

like i know what the terms mean but i just dont know like where to start and how to finish it

Answer 28

12x= 54-6y?
-17x= -62 -6y ?

Answer 29

when you have a system of equations, which is what these problems are, you can solve them by the elimination method (which i did for the first problem), the substitution method (i did for the second), and by using matrices (which aren't really relevant right now, unless you're in honors algebra)

Answer 30

well i dont think ill be in honors anytime soon

Answer 31

is that the next problem?

Answer 32

Solve this system of linear equations. Separate the x- and y-values with a comma.
12x= 54-6y?
-17x= -62 -6y ?

Answer 33

ok

Answer 34

look at the y's. what do you notice about them?

Answer 35

they both have a -6 infront of them

Answer 36

exactly. to use the elimination method, we want to multiply the entire second equation by -1, so that all the signs are changed. that will give us positive 6y. and when we combine the equations, the y will be cancelled out.

so -1(-17x= -62 -6y) is 17x = 62 + 6y

Answer 37

do i need a calculator?

Answer 38

now we have our equations as
12x = 54 - 6y
17x = 62 + 6y

when we combine them, we'll get 29x = 116

Answer 39

a calculator would be helpful :)

Answer 40

see how we completely got rid of the y? now we can solve for x

Answer 41

alright i got a calculator

Answer 42

well my class ends at 2:05 pm and its 1:45 pm now

Answer 43

we're almost done

Answer 44

so 29x = 116. divide both sides by 29 and you get x = 4

Answer 45

alright well im on 4 out of 15 questions

Answer 46

oh.

Answer 47

now that we know what x equals, you can substitute it into either equation to solve for y

Answer 48

12x = 54 - 6y
12(4) = 54 - 6y
48 = 54 - 6y
-6 = -6y
y = 1

Answer 49

so your answer is 4, 1

Answer 50

-17x = -95 -10y
12x =50 -10y

Answer 51

maybe i can help you more after school?

Answer 52

yeah probably cause i have internet at home

Answer 53

see, i don't wanna just work at it myself. i want you to understand what to do

Answer 54

i don't think i'm helping you at all, am i?

Answer 55

ah i understand well thank you for helping me with the answers and i get out of school at 3:40 PM and i normally get home like around 4:20 something

Answer 56

alright. just tag me in any questions :)

Answer 57

how do i tag ?

Answer 58

@ and then my name so @aripotta

Answer 59

alright thanks :)

Answer 60

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