Question

solve the following system of equations 8/x+5/y=9 , 3/x+2/y=4; x not equal 0 ,y not equal 0​

Answer 1

Step-by-step explanation:

Given :-

8/x+5/y=9 ,

3/x+2/y=4;

x ≠ 0 ,y ≠ 0

To find :-

Solve the following system of equations?

Solution :-

Given equations are:

8/x+5/y=9

=> 8(1/x) + 5(1/y) = 9 ----------(1)

3/x+2/y=4

=> 3(1/x) + 2(1/y) = 4 -----------(2)

x ≠ 0 ,y ≠ 0

Put 1/x = a and 1/y = b then

(1)&(2) becomes

8a + 5b = 9 ---------(3)

3a + 2b = 4 ---------(4)

=> 3a = 4-2b

=> a = (4-2b)/3 -----(5)

On Substituting the value of a in (3) then

=> 8[(4-2b)/3] +5b = 9

=> [(32-16b)/3]+5b = 9

=> [(32-16b)+15b]/3 = 9

=> (32-b)/3 = 9

=> 32-b = 9×3

=> 32-b = 27

=> b = 32-27

=>b = 5

On Substituting the value of b in (5) then

a = (4-2(5))/3

=> a = (4-10)/3

=> a = -6/3

=>a = -2

Therefore, a = -2 and b = 5

Now,

a = -2

=>1/x = -2

=> 1 = -2x

=> x = -1/2

and

b = 5

=> 1/y = 5

=> 1 = 5y

=> y = 1/5

Therefore, x = -1/2 and y = 1/5

Answer:-

Solution for the given problem is (-1/2,1/5)

Check:-

If x = -1/2 and y = 1/5 then

LHS =8/x+5/y

=> [8/(-1/2)]+[5/(1/5)]

=> (8×-2)+(5×5)

=>-16+25

=>9

=> RHS

LHS = RHS

and

LHS =3/x+2/y

=> [ 3/(-1/2)]+[2/(1/5)]

=>(3×-2)+(2×5)

=>-6+10

=> 4

=>RHS

LHS = RHS is true for x = -1/2 and y = 1/5

Used Method:-

• Method of Substitution