Question

Solve the following systems of equations:
$\frac{15}{u}+ \frac{2}{v} =17$
$\frac{1}{u}+ \frac{1}{v} =\frac{36}{5}$

Answer 1

Given pair of system of equation :  

15/u + 2/v = 17 …………...( 1 ) 1/u + 1/v = 36/5 …………...( 2)

Let 1/u = x & 1/v = y

Now eq 1 becomes :  

15x + 2y = 17…………..(3)

Eq 2 becomes :  

x + y = 36/5 …………..(4)

From eq 4 :  

y = 36/5 - x ………..(5)

On Substituting the value of y in equation (3) we obtain :

15x + 2y = 17

15x + 2 (36/5 - x) = 17

15x + 72/5 - 2x = 17

13x = 17 - 72/5

13x = (85 - 72)/5

13x = 13/5

x = 13/5 × 1/13

x = ⅕

On putting x = 1/5 in eq (5)  we get :  

y = 36/5 - x

y = 36/5 - ⅕

y = (36 - 1)/5

y = 35/5

y = 7

Therefore , 1/u = x  = ⅕  & 1/v = y = 7

Then , u = 5  & v = 1/6

Hence, the value of the given system of equation is u = 5   and v = 1/6.

Hope this answer will help you…

Some more similar questions from this chapter :  

Solve the following systems of equations:

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1/2x + 1/3y = 2  

1/3x + 1/2y = 13/6

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Answer 2

Answer:

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