Linear equations in two unknows

Let a be the ten digit, b be the unit digit of the number
The number is 10a + b
10a + b = 7(a+b)
10a + b = 7a + 7b
3a - 6b = 0
a - 2b = 0
a = 2b 10a + b - 27 = 10b + a
20b + b - 27 = 12b
21b - 27 = 12b
9b = 27
b = 3
a = 2b = 6
So the number is 63

14 )
Let x be the age of father
Let y be the age of the son
x-10 = 4(y-10)
x -10 = 4y - 40
x = 4y - 30........(1)
x + 10 = 2(y+10)
x + 10 = 2y + 20
x = 2y + 10
Sub (1) in it
4y - 30 = 2y + 10
2y = 40
y = 20
x = 2y+10 = 50

So the father is 50 years old and the son is 20 years old

let x be the unit digit and y be the ten digit
{10y+x=7(x+y)--------(1)
{10y+x-27=10x+y------(2)
From (1), y=2x-----(3)
From (2), y-x=3-----(4)
(3)-(4):x=2x-3
x=3
Sub. x=3 into (1)
10y+x=7(x+y)
10y+3=7(3+y)
3y=21-3
y=6
.'.the number is 63



let x be the PRESENT age of the father, y be the PRESENT age of the son
{x-10=4(y-10)---------------(1)
{x+10=2(y+10)--------------(2)
From (1), x-4y= -30----------------(3)
From(2),x-2y=10-----------------(4)
(3)-(4): -2y=-40
y=20
Sub y= 10 into (1)
x-10=4(y-10)
x-10=4(20-10)
x-10=40
x=50
.'.the present age of the father is 50 and the son is 20