Question

solve for x and y 2/x+3/x =13 and 5/x -4/y=-2​

Answer 1

Step-by-step explanation:

ANSWER:-

(Correct) Given:-

$\dfrac{2}{x} + \dfrac{3}{y} = 13$

$\dfrac{5}{x} - \dfrac{4}{y} = - 2$

So, Let us consider :-

$\dfrac{1}{x} = a$

$\dfrac{1}{y} = b$

So, the equations turn to:-

$2a + 3b = 13$

$5a - 4b = - 2$

Now, multiplying 5 with 1st equation and 2 with second one:-

$5(2a + 3b = 13)$

$10a + 15b = 65 \: \implies(1)$

$2(5a - 4b = - 2)$

$10a - 8b = - 4 \implies(2)$

Now subtracting (1) - (2),

$10a + 15b - (10a - 8b) = 65 - ( - 4)$

$\cancel{10a} + 15b - \cancel{10a} + 8b = 69$

$23b = 69$

$\boxed{b = 3}$

Now,

$2a + 3(3) = 13$

$2a = 13 - 9$

$2a = 4$

$\boxed{a = 2}$

Now,

$\dfrac{1}{x} = 2$

$\boxed{x = \dfrac{1}{2} }$

And,

$\dfrac{1}{y} = 3$

$\boxed{y = \dfrac{1}{3} }$