Respuesta :

mhanifa

Answer:

x = 1

y = 1

Step-by-step explanation:

Given:

  • x/a + y/b = 1/a + 1/b
  • x/a - y/b = 1/a - 1/b

Add up the two equations side-by-side, this will cancel y/b and 1/b:

  • x/a+x/a = 1/a+1/a
  • 2x/a=2/a
  • x = 1

Subtract the  two equations side-by-side, this will cancel x/a and 1/a:

  • y/b+y/b = 1/b+1/b
  • 2y/b=2/b
  • y=1
Hrishii

Answer:

x = 1, y = 1

Step-by-step explanation:

[tex] \frac{x}{a} + \frac{y}{b} = \frac{1}{a} + \frac{1}{b} .....(1) \\ \frac{x}{a} - \frac{y}{b} = \frac{1}{a} - \frac{1}{b} .....(2) \\ \\ let \: \: \frac{1}{a} = m, \:\:\&\: \: \frac{1}{b} = n \\ so \: equatin \: (1) \: reduces \: to: \: \\ \\ so \: equatin \: (1) \: reduces \: to: \: \\ mx + ny = m + n....(3)\\ and \: equatin \: (2) \: reduces \: to: \: \\ mx - ny = m - n....(4) \\ adding \: equations \: (3) \: (4) \\ mx + ny = m + n \\ mx - ny = m - n \\ - - - - - - - - - - \\ 2mx = 2m \\ x = \frac{2m}{2m} \\ \huge \red{ \boxed{x = 1}} \\ substituting \: x = 1 \: in \: equatin \: (3) \\ m \times 1 + ny \: = m + n \\ m + ny \: = m + n \\ ny = m + n - m \\ ny = n \\ y = \frac{n}{n} \\ \huge \purple{ \boxed{y = 1}}[/tex]