Question

Find the values of x and y for the given pair of linear equations :
(14/2x+y) + (3/2x-y)=5 and (3/2x=y)-(4/2x-y)= -25/7
where x ≠ 0, y ≠ 0 and y ≠ 2x.

Answer 1

here is your answer by Sujeet,

Let to be 1/2x+y=a
1/2x-y=b

So,
14a+3b=5 *3
3a-4b=-25/7 *14
by elimination method,
42a+9b=15
42a-56b=-50
-------------------+
65b=65
b=65/65
b=1

Now putting the value of b in another equation,
14a+3b=5
14a+3=5
14a=5-3
14a=2
a=2/14
a=1/7

Now putting the
1/2x+y=1/7
2x+y=7. --------(5)

Again,

1/2x-y=1
2x-y=1 ---------(6)

by elimination method
2x+y=7. *2
2x-y=1. *2

4x+2y=14
4x-2y=2
-------------
4y=12
y=12/4
y=3

Again,
2x+y=7
2x+3=7
2x=7-3
2x=4
x=4/2
x=2


that's all

Sujeet

Answer 2

first solve brackets of 1st equation you will get 17/x=6 therefore x=17/5
now similarly solve brackets of second equation you will get 2xy/2x=25/7-2 therefore y=18/7