substitution method) y= 6-x & 2x-3y=-2 i need alot of help?

Question

i m been trying to get these problems but my head just starts to hurt when i look at the paper

Answer 1

if y = 6-x
then you just put that in for y
2x-3(6-x) = -2
2x- 18 + 3x = -2
5x - 18 = -2
5x = -20
x = -4

Answer 2

were you given a value(number) for either x or y? If not first remember that you have to get all the xs and ys on opposite sides of the eqaution. Next, solve for one then when you get that number solve for the other.
lets do the harder one first (2x-3y=-2):
1) move the the 2x over to the side with -2 this will give you: -3y=-2-2x (whenever you move a number over to the other side of the = sign, the sign (+/-) infron of it changes)
2) becasue you don't want to work with a negative, multiply the whole eqution by -1 whihc gives you: 3y=2+2x
3) Now, using subsitution insert (6-x) wherever you see a y:
3(6-x)=2+2x
4)now solve: 18-3x=2+2x
5) again, gropu alike numbers togtehr on either side of the eqaution(remember whenever you move a number to the other side of the equation its sign changes): 18-2=2x+3x
6) Now solve for x: 16=5x therefore x=(16/5)
now that you have a value for x, plug it into the equation: y=6-x to solve for y: y=6-(16/5)
7) so that you can subtract a whole number and a fraction multiply the whole number by the dinominator (bottom number) of the fraction: 6*5=30 so now you know that 30 5s is equal to 6
8) now subtratct the numbers to finally get your answer for y: (30/5)-(16/5)=(14/5) therefore y=(14/5)
if you want to check that your answers are correct, plug in the final answer you got for x and y into the equation (use the shorter eqaution to make it easier)
check:
1) y=6-x where x=(16/5) and y=(14/5) [rember that 6=(30/5)]
(14/5)=(30/5)-(16/5)
2) This checks as (14/5)=(14/5) so you know that the answer you got for y is correct
3) Now to check for x, use that same eqaution but change it so that you have x=something: y=6-x is changed to x=6-y
4) Now just plug in the numbers again: x=(16/5) and y=(14/5) [rember that 6=(30/5)]
5) (16/5)=(30/5)-(14/5) this too checks as (16/5)=(16/5) so the answer for x is correct
I don't know if they want you keep the answer in fractions, it's just easier to work this way than working with a mixed fraction
x=3 and (1/5) y=2 and (4/5)

You just need to breathe before you even start....I know math can be a bit confusing, especially this type of math, but remember tehy're just numbers and they can't hurt you. Good luck in school :)

Answer 3

x=4 y=2

Answer 4

Hi,
You know that y = 6-x so substitute y by 6-x within the 2nd equation. This then becomes:

2x-3(6-x)=-2 which leads to 2x-18+3x=-2
which leads to 5x -18 = -2 or 5x = 16 so that x= 16/5

Filling this into the 1st equation leads to:
y=6- 16/5 or y=30/5 - 16/5 so that y = 14/5

Regards,
Walter

Answer 5

y=6-x
2x-3y=2 Solve for x first, substitute 6-x for y in the second equation

2x-3(6-x)=2
2x-18+3x=2
5x-18=2
5x=20
x=4

substitute 4 for x in either equation to find y

y=6-4
y= 2

(x=4, y= 2 ) check answers in both equations by substituting 4 and 2 in place of x and y in the equations.

2=6-4

8-6+2

x=4. y=2

Answer 6

Okay, take your time and go through each line, making sure you understand each before going to the next.

y=6-x
2x-3y=-2

So, since y=6-x,
2x-3(6-x)=-2. Expanding,
2x-18+3x=-2. Grouping the x's on one side and the numbers on the other,
5x=16
x=16/5=3 1/5
y=6-x=6-3.2=2.8

Answer 7

x= 16/5

y=6-x so 2x-3y= -2 is the same as 2x-3(6-x) = -2

2x-18+3x = -2

2x + 3x = 16

5x = 16

x= 16/5

edit: jennifer and I are the only correct answers, everyone else is confusing you or getting the wrong answer...amazing. Glen is right too

Answer 8

if y=6-x and 2x-3y=-2, then 2x-3(6-x)=-2.
then you expand: 2x-18+3x=-2
then remove the -18: 2x+3x=16
2x+3x is just 5x, so : 5x=16
divide by 5: x=16/5 or x=3.2

Answer 9

ok, if y = 6-x, you substitute 6-x wherever you see y.

so, your new equation would look like this:
2(6-x) - 3(6-x) =-2
which then turns into:
12-2x-18-3x=-2
which then turns into:
-6-5x=-2
which then turns into:
-5x=4
which then means that x=-4/5

Answer 10

I just checked your question page, and it seems you are asking a lot of these. You will never learn how to do them if you just copy from the internet...hopefully, all the answers are wrong, but I doubt it. Now, stop making excuses and learn! These are so easy, and later they DO get harder. So learn the easy stuff now!