Question

Help please.
Use the method of substitution to solve the system of liner equations.
2x-y=3
7x-3y=14
The solution is? Type an ordered pair.

Answer 1

solve the first equation for y,\[y=2x-3\]
Now that you know what y is, substitute that into equation 2 and solve for x. Once you have x plug it into equation 1 and obtain y. Do you think you can do this from this explanation?

Answer 2

I really need help in the steps as I am not good at these equations at all. If you have time to help me. please.

Answer 3

sure lets start at the beginning. Solve the first equation for one of the variables. I chose to solve for y because it doesn't have a coefficient and it will be less messy.

Answer 4

add y to both sides of the equation.\[y+2x-y=3+y\]You can see that the y's will cancel and you will be left with \[2x=y+3\]

Answer 5

next subtract e from both sides \[2x-3=y+3-3; y=2x-3\]

Answer 6

remember if you do the same thing to each side of the equation essentially nothing changes

Answer 7

Now that we know y plug it into the 2nd equation.\[7x-3(2x-3)=14\]

Answer 8

(still listening and taking notes as you go along) :)

Answer 9

I prefer to write everything using addition and negative numbers. It helps me to not make mistakes in sign changes. \[7x+(-3)(2x+(-3))\]distribute the -3. \[7x+[(-3\times2x)+(-3\times-3)]=14\]

Answer 10

Now we should have \[7x+(-6x)+9=14\]We can simplify further to \[x+9=14\]

Answer 11

what do you think we do next to solve for x??

Answer 12

add 14 to both sides?

Answer 13

Keep in mind that our goal is to get x by itself on one side of the equation.

Answer 14

try again...

Answer 15

9 to both sides?

Answer 16

add or subtract??

Answer 17

subtract

Answer 18

Correcttt!!!!!!!

Answer 19

so we should arrive at \[x=5\]

Answer 20

Wow, i surprised my own self LOL

Answer 21

But we still need to find y. It is helpful when working these problems to put a star by our first equation we simplified which was \[y=2x-3\]This will help us go back and find it faster.

Answer 22

Now that we know the value for x what do you think we have to do to solve for y??

Answer 23

i'm not exactly sure, but I am guessing we have to plug 5 in somewhere. near the x i'm thinking.

Answer 24

because x=5 we can plug it into the equation \[y=2x-3\] and solve

Answer 25

What did you get for the answer??

Answer 26

y=7?

Answer 27

Correcttt Againnnn!!!!

Answer 28

:)

Answer 29

So, to put those in ordered pair.
x=5
y=7

Answer 30

Now what was the last part of the question? Do you have to write the answer as an ordered pair?

Answer 31

(5,7)?

Answer 32

(x, y) that is the format of an ordered pair

Answer 33

yup

Answer 34

Do you understand algebra steps a little bit better??

Answer 35

THANK YOU!!!!!
Thanks for taking the time to TEACH me and not blurt out the answer. :)

Answer 36

algebra is just a bunch of rearranging equations to look prettier but essentially the original equation is deep inside still. Like a girl that wears too much make up

Answer 37

You're welcome

Answer 38

Stevns, while we are here if I post a problem in this box will you check my answer?

Answer 39

sure

Answer 40

The perimeter of a rectangle is 38 ft. The length is 3 ft longer than the width. Find the dimensions. Write a system of linear equations and solve the resulting system. Let x be the length and y be the width.
Write the first equation.
2x+2y=(38)
Write the second equation.
X=y+(8)
What is the length? ( 11 _) ft
What is the width? ( 8 ) ft

Check the answers in the ( ) for me please :)

Answer 41

I don't want to get any of it wrong LOL

Answer 42

or maybe x=y+3, not 8. now i'm doubting myself lol

Answer 43

I would use the letters w and l not to get confused. The numbers are correct. How did you get 8 for the second equation. I was thinking \[l=w+3\]Because the length is 3 more than the width

Answer 44

so three is right not 8. i am glad i asked. i knew something looked wrong lol

Answer 45

if you plug l= w + 8 into the equation (like the last problem we worked) it doesnt work out... Ya good thing you asked. You can always work the problem backwards when you're done to check your work.

Answer 46

Can you check one last one? I PROMISE! lol

Answer 47

omg. lol

Answer 48

A tugboat goes 120 miles upstream in 20 hours. The return trip downstream takes 10 hours. Find the speed of the tugboat without a current and the speed of the current.
The speed of the tugboat is ( 9 ) mph, and the speed of the current is ( 3 ) mph.

Answer 49

I don't want to fail and your a good teacher/checker! LOL :)

Answer 50

speed is distance over time. Upstream the boat is fighting the current and downstream it is with the current so I would setup my equations like this.

Let b stand for the speed of the boat and c stand for the speed of the current.\[b \frac{ mi }{ hr }-c \frac{ mi }{ hr }=\frac{ 120mi }{ 20hr }\]\[b \frac{ mi }{ hr }+c \frac{ mi }{ hr }=\frac{ 120mi }{ 10hr }\]

Answer 51

so simpler\[b-c=6;b+c=12\]since all the units are the same we can add the numbers without worry.

Answer 52

Which I get 6 and 12

Answer 53

solve for one variable and substitute and I get 9 for boat and 3 for current like YOOOUUUU

Answer 54

YOU rule! i WISH i COULD give you a 1,000,000 medals. :)
HUGS!

Answer 55

You're welcome. I'm just watching football no big deal.

Answer 56

LOL! I hope your team wins!

Answer 57

THANK YOU!

Answer 58

what class r u taking

Answer 59

Algebra I and i'm not the brightest student in the class. LOL (as you can see why i'm here) :)

Answer 60

everybody learns at their own pace. I am usually lost til a switch is flipped. You just need to find that switch. You'll be fine. You'll get out of it what you put in, sounds like you're trying hard.

Answer 61

Good Luck!

Answer 62

Thanks so much. :) --- See you around i'm sure. Have a goodnight.

Answer 63

hey, I need help, just tell me the because I'm on homebound and I just wanna get it done... I hate math with a passion. here's the equations.
Complete the following ordered pairs for the equation. 6x + -5y = 20 (_, -4) (_, 2)