Solve the following system of equations:8v−3u=5uv6v−5u=−2uv

Question

Solve the following system of equations:

8 v - 3 u = 5 u v

6 v - 5 u = - 2 u v

Options:

A . u=0,v=0

B . u=2231,v=1123

C . Both A and B

D . u=3122, v= 2311

Answer: Option B
:
B
Divide the given equations by uv,

8 v - 3 u = 5 u v \Rightarrow \frac{8}{u} - \frac{3}{v} = 5 . . . (1)

6 v - 5 u = - 2 u v \Rightarrow \frac{6}{u} - \frac{5}{v} = - 2 . . . (2)

Assume

\frac{1}{u} = x

and

\frac{1}{v} = y

Put the values of

\frac{1}{u}

and

\frac{1}{v}

in (1) and (2)

8 x - 3 y = 5 . . . (3)

6 x - 5 y = - 2 . . . (4)

Solving equations (3) and (4) we get x and y
Multiply (3) with 5 and (4) with 3 to equate the coefficients of y.

40 x - 15 y = 25

18 x - 15 y = - 6

Solve The Following System Of Equations:8v−3u=5uv6v−5u=�...

\Rightarrow x = \frac{31}{22} \Rightarrow u = \frac{22}{31}

Substituting x in (3)

8 \times \frac{31}{22} - 3 y = 5 \to 3 y = \frac{69}{11}

\to y = \frac{23}{11} \Rightarrow v = \frac{11}{23}

So,

u = \frac{22}{31}

and

v = \frac{11}{23}

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