Question

solve the following systems of equations by using the method of sublimation substitution
1)
2 X + 3 Y =9,3x+4y=5
2)
2x/a-y/b=2,x/a-y/b=4

Answer 1

Soln 1 : 2x + 3y = 9

x = (9 - 3y)/2 __(i)

and, 3x + 4y = 5 __(ii)

On substituting (i) in (ii) we get,

→ 3(9 - 3y)/2 + 4y = 5

→ (27 - 9y + 8y)/2 = 5

→ 27 - y = 10

→ y = 17

Therefore, x = (9 - 3(17))/2

→ x = - 21

Hence x is - 21 and y is 17.

______________________________

Soln 2 : Let find out value of x/a,

→ x/a - y/b = 4

→ x/a = 4 + y/b

     ↓

→ 2x/a - y/b = 2

→ 2(4 + y/b) - y/b = 2

→ 8 + y/b = 2

→ y/b = - 6

         ↓

Therefore x/a = 4 - 6 = - 2

Hence x/a is - 2 and y/b is - 6.

Answer 2

hey mate

here is your answer..

1)-

equ 1- 2x+3y=9

=>2x=9-3y

=>x=(9-3y)/2

substituting the value of x in equ 2.

where equ 2- 3x+4y=5

=>3*(9-3y)/2 +4y=5

=>((27-9y)+8y)/2=5

=>27-y=10

=>y=27-10

=>y=17

thus,

x=(9-3y)/2

x=(9-3*17)/2

x=(9-51)/2

x=-42/2=-21

thus, (x,y)={-21,17)

-----++++-----+++++-------+++++--------

2)-

equ 1- 2x/a-y/b=2

=>2x/a=2+y/b

=>x/a=½(2+y/b)

substituting the value in equ 2 where equ 2 is x/a-y/b=4

thus,

=>½(2+y/b)-y/b=4

=>1+1/2*y/b-y/b=4

=>-y/2b=3

=>y/b=-6

thus,

x/a=½(2+y/b)

=>½(2+(-6))

=>½(2-6)

=>½*-4

=>-2

thus

(x/a,y/b)={-2,-6}