Question

Sᴏʟᴠᴇ ɪᴛ ʙʏ sᴜʙsᴛɪᴛᴜᴛɪᴏɴ ᴍᴇᴛʜᴏᴅ​

Answer 1

x = 1, y = 1

Explanation:

`(x)/(a) + (y)/(b) = (1)/(a) + (1)/(b) .....(1) \\ (x)/(a) - (y)/(b) = (1)/(a) - (1)/(b) .....(2) \\ \\ let \: \: (1)/(a) = m, \:\:\&\: \: (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 = (2m)/(2m) \\ \huge \red{ \boxed{x = 1}} \\ substituting \: x = 1 \: in \: equatin \: (3) \\ m * 1 + ny \: = m + n \\ m + ny \: = m + n \\ ny = m + n - m \\ ny = n \\ y = (n)/(n) \\ \huge \purple{ \boxed{y = 1}}`

Answer 2

x = 1

y = 1

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