Question

HELP!!! PLEASE
how would you solve this with out getting a decimal i have tried but no answer i got was right, 5u+2v=18 and 6u+v=22 .

Answer 1

What do you mean "without getting a decimal"?
If a decimal value is the answer, then that's the answer...

Would you rather write it as a fraction or something?

Answer 2

my teacher told us its not going to be a decimal answer

Answer 3

Oh I see :)

Answer 4

\[\large\rm 5u+2v=18\]\[\large\rm 6u+~~v=22\]Personally I really like the elimination method:
We try to match up one of the variables in each equation,
and then subtract.

Answer 5

yeah... its to be done using substuiton method but i dont really get that either

Answer 6

Substitution? Fine fine fine :p

Answer 7

Notice the v in the second equation has no fancy coefficient.
So it will be easy to write it in terms of v=(stuff)

Answer 8

\[\large\rm 6u+v=22\]How bout we subtract 6u from each side, ya?

Answer 9

yes i am

Answer 10

but the problem it 22 not 23

Answer 11

This system, the way you wrote it, has ugly decimal values for a solution.

Answer 12

23 would make it a nice problem

Answer 13

ohhhkay ill tell my teacher in the morning about thais maybe i wont have to do this

Answer 14

ohhhkay ill tell my teacher in the morning about thais maybe i wont have to do this

Answer 15

XD

Answer 16

well, i still suggest doing it if it were 23

Answer 17

good practice

Answer 18

okay
ill try it with 23

Answer 19

\[\large\rm 6u+v=23\]In the second equation,
subtracting 6u from each side gives us,\[\large\rm v=23-6u\]understand that step?

Answer 20

yeah

Answer 21

This equality sign is telling us that \(\large\rm \color{orangered}{v}\) is the same as \(\large\rm \color{orangered}{(23-6u)}\).

\[\large\rm 5u+2\color{orangered}{v}=18\]
So do you understand how we can use this with our other equation?

Answer 22

not really but i think i can do that

Answer 23

We can replace the v in our first equation with 23-6u because those things are equivalent,\[\large\rm 5u+2\color{orangered}{(23-6u)}=18\]

Answer 24

From that point,
you have an equation involving only u,
no more v,

so you can do some quick steps and solve for u.

Answer 25

okay

Answer 26

Here is a simpler way
In the beginning you said that we can rewrite the equation to (v=23-6u)
We can also rewrite 5u+2v=18 to 2v=18-5u
So we should now have the two equation of
v=23-6u and
2v-18-5u
This means that 2(23-6u)=18-5u
It can simplify to 46-12u=18-5u
And then you just solve.
46=18+7u
28=7u
u=4
Then just plug it into the equation to find v.
You don't have to do it this way, but I just really wanted to say it :D
It's good review for SAT.

Answer 27

thanksguys !!!!:)