how do i find 2 unknowns with fractions in equations?

Question

R=1, e = 1.54, Vt= 1.4,

I= e/ (r + R) ------>{eq, 1}
Vt = e - Ir ---------->{eq.2}

find I and r?

tnx,. pls include the solutions and the type of equation you used.. if its substitution or elimination.. etc..


tnx

Answer 1

substitution: substitute for I in eq. 2, since you know that I=e/(r+R). Then you can solve for r. when you get that, go back to eq. 1 and plug in the numbers

Answer 2

Substitute values in the equation. Start with eq #2

1.4=1.54 - (Ix1)

since anything times 1 is the same value

1.4 = 1.54- I
Moving the value from one side of the eq to other

1.4-1.54 = -I

-0.04 =-I

therefore I = 0.04

Now substitute this and other values in eq 1

0.04 = 1.54/ (r+1)

0.04 x (r+1) = 1.54
r+1 = 1.54/0.04
r+1 = 38.5
r=38.5-1
r = 37.5

Two unknowns: I = 0.04 and r = 37.5

Hope this helps!

Answer 3

well, start by substituting the provided values to get the real two equations

L= 1.54 / (r+1)
1.4=1.54-Lr

now you have two equations with two unknowns
there are several techniques to solve simultaneous equations

I suggest substitution, substitue the expression for L in the first equation in for L in the second equation

1.4 = 1.54 - (1.54/(r+1))

now you have one equation with one unknown
you should be able to do the algebra, it might start like this:

subtract 1.54 from both sides ---> -.04 = -1.54/(r+1)

multiply (r+1) by both sides ---> -.04 r -.04 = -1.54

add .04 ---------------------------> -.04 r = -1.5

divide by -.04 -----------------------> r = 37.5

go back and substitue r somewhere to get the value of L

good luck,
keep at it

Answer 4

I = e/r+R = I = 1.54/r+1 (substituting given values)

Vt = e - Ir =1.4 = 1.54 -r (substituting given values)

Then sub 1.54/r+1 for I

Then 1.4 =1.54- r(1.54/r=1) then rearranging,

1.4 - 1.54 = -r(1.54/r+1) transpose, 1.4 - 1.54 = -r(1.54/r+1)

so -0.14 = -1.54r/(r+1) cross multiply , and

-1.4r -.14 = -1.54r and, 1.4r = 0.14 , r = 0.1

ergo , I = 1.54/1.1 = 1.4 Cheers

Answer 5

Multiply the equation with fractions by the denominator of the fraction; that will get rid of the fraction:

I=e/(r + R)

I*(r + R) = e

I*r + I*R = e

Now you should be able to solve the equations by the usual methods.