SOLVING SYSTEM OF EQUATIONS WITH FRACTIONS BY ELIMINATION

The flow chart shown below explains the steps to be done in solving system of linear equations with two unknowns 'x' and 'y' using elimination method. 

Solved Examples

Question 1 :

Solve the following system of linear equations by elimination method.

15/x  +  2/y  =  17

1/x  +  1/y  =  36/5

Solution :

Let a  =  1/x  and  b  =  1/y. 

Then, 

15a  +  2b  =  17 -----(1)

a  +  b  =  36/5 -----(2)

(1) - 2(2) : 

13a  =  17 - 72/5

13a  =  (85 - 72) / 5

13a  =  13/5

Divide each side by 13. 

a  =  1/5 -----(3)

Substitute 1/5 for a in (1). 

(1)-----> 15(1/5) + 2b  =  17

3 + 2b  =  17

Subtract 3 from each side. 

2b  =  14

Divide each side by 2.

b  =  7 ----->(4)

In (3) and (4), substitute 1/x for 'a' and 1/y for b.  

Question 2 :

Solve the following system of linear equations by elimination method

   2/x + 2/3y  =  1/6

3/x + 2/y  =  0

Solution :

Let a  =  1/x  and  b  =  1/y. 

Then, 

2a  +  2b/3  =  1/6 -----(1)

3a + 2b  =  0 -----(2)

3(1) - (2) : 

3a  =  1/2

Divide each side by 3. 

a  =  1/6 -----(3)

Substitute 1/6 for a in (2). 

(2)-----> 3(1/6) + 2b  =  0

1/2 + 2b  =  0

Subtract 1/2 from each side.

2b  =  -1/2

Divide each side by 2.

b  =  -1/4 -----(4)

In (3) and (4), substitute 1/x for 'a' and 1/y for b.  

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