Question

solve by elimination method : 5/x+6y=13 & 3/x+4y=7

Answer 1

5 = 13x + 78y -(1)
3 = 7x + 28y -(2)

13x + 78y = 5 -(1)
7x + 28y = 3 -(2)

multiplying 1st equation by 7 and 2nd by 13

91x + 546y = 35
91x + 364y = 39
(-) (-) (-)
------------------------
182y = -4
y = -2/91

Putting the value of y in 1st equation

13x + 78y = 5
13x + (78 * -2/91) = 5
13x - 12/7 = 5
13x = 47/7
x = 47/91

x = 47/91 and y = -2/91

Answer 2

Answer:

putting 1/x=u the given equation become

5u+6y=13 ……(1)

3u+4y=7 ……(2)

multiply (1) by 3 and (2) by 5 on subtracting we get

15u+18y=39

15u+20y=35

- - -

………………………

-2y=4

y=-4/2

y=-2

putting y=-2 in (1) we get

5u+6(-2)=13

5u-12=13

5u=13+12

5u=25

u=25/5

u=5

Now, u=5. 1/x=5

5x=1

x=1/5

hence x=1/5 and y=-2