functions of equations

Let the two digit number be 10x+y
then, we have
x2 + y2 = 50 ---- (1)
and
10y + x = ( 10x + y ) - 54
that is, 9x - 9y = 54
x - y = 6 ---- (2)
sub x = y + 6 into (1) gives
(y+6)2 + y2 = 50
2y2 + 12y + 36 - 50 = 0
y2 + 6y - 7 = 0
y = 1 or -7 (rejected)
x = y + 6 = 7
Thus the two-digit number is 71
Remarks: 十進制數字
abcd = a*1000 + b*100 + c*10 + d
This is what we called "place value"(位值)

Let the 10th digit be x and the unit digit be y.
So the original value of the number = 10x + y,
when reversed, the value of the number becomes 10y + x,
so (10x + y) - (10y + x) = 54
9x - 9y = 54
x - y = 6 or x = 6 + y.
also, x^2 + y^2 = 50
that is (6 +y)^2 + y^2 = 50
36 + 12y + 2y^2 - 50 = 0
2y^2 + 12y - 14 = 0
y^2 + 6y - 7 = 0
(y +7)(y-1) = 0
y = -7(rej.) or y = 1
when y = 1, x = 6 + y = 7.
so the number is 71.