SOLVING SYSTEMS OF EQUATIONS BY ELIMINATION WITH DIFFERENT COEFFICIENT

Solved Problems

Problem 1 : 

Solve :

3(2x + y)  =  7xy

3(x + 3y)  =  11xy

Solution :

3(2x + y)  =  7xy 

6x + 3y  =  7xy

Divide both sides of the equation by xy. 

(6/y) + (3/x)  =  7

Let a  =  1/x  and  b  =  1/y.

3a + 6b  =  7 -----(1)

3(x + 3y) = 11xy

3x + 9y  =  11xy

Divide both sides of the equation by xy. 

 (3/y) + (9/x)  =  11

 9a + 3b  =  11 -----(2)

(1) - 2(2) :

-15a  =  -15

a  =  1 -----(3)

Substitute a  =  1 in (1). 

3(1) + 6b  =  7

6b  =  7 - 3

6b  =  4

b  =  2/3 -----(4)

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

So, the solution is

(x, y)  =  (1, 3/2)

Problem 2 : 

Solve :

(4/x) + 5y  =  7

(3/x) + 4y  =  5

Solution :

Let a  =  1/x and b  = y

Then,

4a + 5b  =  7 -----(1)

3a + 4b  =  5 -----(2)

4(1) - 5(2) :

a  =  3 -----(3)

Substitute a  =  3 in (1). 

(1)-----> 4(3) + 5b  =  7

12 + 5b  =  72

5b  =  -5

b  =  -1 -----(4)

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

So, the solution is

(x, y)  =  (1/3, -1)

Problem 3 : 

Solve :

13x + 11y = 70

11x + 13y = 74

Solution :

13x + 11y  =  70 -----(1)

11x + 13y  =  74 -----(2)

(1) + (2) :

x + y  =  6 -----(3)

(1) - (2) :

x - y  =  -2 -----(4)

(3) + (4) :

x  =  2

Substitute x  =  2 in (3). 

(3)-----> 2 + y  =  6

y  =  4

So, the solution is

(x, y)  =  (2, 4)

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