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Let, the two numbers be X and Y
Case : 1) according to question
X/Y = 5/7
7X - 5Y = 0 _ eq. 1
Case : 2) according to question
X+6/y+6 = 7/9
9X + 54 =7Y + 42
9X - 7Y = - 12 _ eq. 2
Multiply by 7 in eq. 1 and by 5 in eq. 2 then, sub. both equation
49X - 35Y = 0
45X - 35Y = - 60
- + +
4X +0 = 60
4X = 60
X = 15
Put the value of X in eq. 1
7*15 - 5Y =0
105 =5y
Y = 21
Case : 1) according to question
X/Y = 5/7
7X - 5Y = 0 _ eq. 1
Case : 2) according to question
X+6/y+6 = 7/9
9X + 54 =7Y + 42
9X - 7Y = - 12 _ eq. 2
Multiply by 7 in eq. 1 and by 5 in eq. 2 then, sub. both equation
49X - 35Y = 0
45X - 35Y = - 60
- + +
4X +0 = 60
4X = 60
X = 15
Put the value of X in eq. 1
7*15 - 5Y =0
105 =5y
Y = 21
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