How to Solve bu using elimination method ?

5/(x+y) + 2/(x-y) = 3
20/(x+y) - 3/(x-y) = 1

3 Answers
Jun 4, 2018

x=-11/2,y=-9/2

Explanation:

Substituting
a=1/(x+y),b=1/(x-y)
so we have the System
5a+2b=3
20a-3b=1
Multiplying the first equation by -4 and adding to the second we get
b=-1
so
a=-1/10
Then we have
1=-x+y
-10=x+y
from here we get
x=-11/2
y=-9/2

Jun 4, 2018

x = 3 and y = 2

Explanation:

5/(x + y) + 2/(x - y)=3

20/(x + y)-3/(x - y)= 1

Let;

1/(x + y) = a and 1/(x - y) = b

Therefore;

5/(x + y) + 2/(x - y)=3

5(1/(x + y)) + 2(1/(x - y))=3

5a + 2b = 3 - - - eqn1

Similarly..

20/(x + y)-3/(x - y)= 1

20(1/(x + y))-3(1/(x - y)) = 1

20a - 3b = 1 - - - eqn2

Using Elimination Method!

5a + 2b = 3 - - - eqn1

20a - 3b = 1 - - - eqn2

Multiply eqn1 by 3 and eqn2 by 2

3(5a + 2b = 3)

2(20a - 3b = 1)

15a + 6b = 9 - - - eqn3

40a - 6b = 2- - - eqn4

Adding both eqn3 and eqn4 together..

(15a + 40a) + (6b + (-6b))= 9 + 2

55a + 6b - 6b = 11

55a = 11

a = 11/55

a = 1/5

Substituting the value of a into eqn1

5a + 2b = 3 - - - eqn1

5(1/5) + 2b = 3

cancel5(1/cancel5) + 2b = 3

1 + 2b= 3

2b = 3 - 1

2b = 2

b = 2/2

b = 1

But;

1/(x + y) = a and 1/(x - y) = b

a = 1/(x + y)

1/5 = 1/(x + y)

Cross multiplying;

1(x + y) = 1(5)

x + y = 5 - - - eqn5

Similarly..

b = 1/(x - y)

1 = 1/(x- y)

1/1 = 1/(x- y)

Cross multiplying;

1(x - y) = 1(1)

x - y = 1 - - - eqn6

Solving simultaenously again..

x + y = 5 - - - eqn5

x - y = 1 - - - eqn6

Using Elimination Method!

Adding eqn5 and eqn6 together;

(x + x) + (y +(-y)) = 5 + 1

2x + y - y = 6

2x = 6

x = 6/2

x = 3

Substituting the value of x into eqn6

x + y = 5 - - - eqn5

3 + y = 5

Collecting like terms;

y = 5 - 3

y = 2

Hence;

x = 3 and y = 2

Jun 4, 2018

x=3,y=2

Explanation:

5/(x+y)+2/(x-y)=3
20/(x+y)-3/(x-y)=1

Let x+y be a and x-y be b

:.5/a+2/b=3----------(1)

:.20/a-3/b=1-----------(2)

:.(1) xx 4

:.20/a+8/b=12------(3)

:.(2)-(3)

:.-11/b=-11/1

:.b/-11=1/-11

multiply both sides by-11

:.b=-11/-11

:.b=1

substitute b=1 in (1)

:.5/a+2=3

:.5/a=3-2

:.5/a=1

:.a/5=1

multiply both sides by 5

:.a=5

:.a=x+y=5-----(4)

:.b=x-y=1------(5)

:.(4)+(5)

:.2x=6

:.x=6/2

:.x=3

:.3+y=5

:.y=5-3 in (4)

:.y=2