Question

Solve the following systems of equations:
$\frac{1}{2x}+ \frac{1}{3y} =2$
$\frac{1}{3x}+ \frac{1}{2y} =\frac{13}{6}$

Answer 1

Given pair of system of equation :  

1/2x + 1/3y = 2 …………...( 1 )

1/3x + 1/2y = 13/6 …………...( 2 )

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

Now eq 1 becomes :  

u/2 + v/3 = 2

(3u + 2v)/6 = 2

3u + 2v = 2 × 6

3u + 2v = 12 …………..(3)

Eq 2 becomes :  

u/3 + v/2 = 13/6

(2u + 3v)/6 = 13/6

2u + 3v = 13/6 × 6

2u + 3v = 13 …………..(3)

Elimination method is used to solve this Linear pair of Equations:

On multiplying eq 1 by 2 and eq 2 by 3 :  

6u + 4v = 24 …………..(4)

6u + 9v = 39………..(5)

On subtracting equation (5) from (4) :

6u + 4v = 24

6u + 9v = 39

(-) (-)  (-)

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 - 5 v = - 15  

v = 15/5

v = 3  

On putting v = 3 in eq (3)  we get :  

3u + 2v = 12

3u + 2 × 3 = 12

3u + 6 = 12

3u = 12 - 6

3u = 6

u = 6/3

u = 2  

Therefore , 1/x = u  = 2 & 1/y = v = 3

Then , x = ½ & y = ⅓

Hence, the value of the given system of equation is x = ½    and y = 1/3.

Hope this answer will help you…

 

Some more similar questions from this chapter :  

Solve the following systems of equations:

1/7x + 1/6y = 3  

1/2x - 1/3y = 5  

brainly.in/question/17131588

 

Solve the following systems of equations:

x + y/2 = 4  

x/3 + 2y = 5

brainly.in/question/17132545

Answer 2

Answer:

Hope it helps you.....