Question

Find x and v in terms of c and b:
(x/c)+(v/b)=1
(x/b)+(v/c)=1
x=?
v=?

Answer 1

So what exactly is this answer for this? I'm still confused with this.

Answer 2

just with pencil and paper i get
\[x=\frac{bc}{b+c}\]

Answer 3

i will write the steps but let me check it first

Answer 4

Isolate v first
then plug it into the second equation

Answer 5

yeah looks good to me

Answer 6

\[v = b(1-\frac{x}{c})\]

Answer 7

\[\frac{x}{b}+\frac{b(1-\frac{x}{c})}{c} = 1\]

Answer 8

\[xc +b^{2}(1-\frac{x}{c})=bc\]

Answer 9

i did this

\[bx+cv=bc\]
\[cx+bv=bc\]
\[b^2x+bcv=b^2c\]
\[c^2x+bc^2=bc^2\] subtract to get
\[(b^2-c^2)x=b^2c-bc^2=bc(b-c)\]
\[x=\frac{bc(b-c)}{b^2-c^2}=\frac{bc(b-c)}{(b-c)(b+c)}=\frac{bc}{b-c}\]

Answer 10

you can also use cramer's rule i guess. oh and since this is symmetric in x and v, you get the same thing for v

Answer 11

Shouldn't it be b+c ?