Problem : What are our ages now? Problem : 
My age was twice your age , when I was the 
same age as yours now. And when you are the 
same age as mine now ,  the sum of our ages is 
$63$ .
What are our ages now?
I see this problems in my teacher and solution is 
$(28,21)$
But I don't know how I solve it ! 
Please if any one have ideas drop here to see 
Thanks!
 A: Let your age be $x$. If the age difference is $\Delta x$, in $\Delta x$ years our ages will sum to 63, so we have $2x+\Delta x = 63$, which is to say $\Delta x = 63-2x$. 
We also know that $\Delta x$ years ago you were twice my age, so $x-\Delta x = 2(x-2\Delta x)$ or $3\Delta x = x$. 
$$3\cdot 63 -6x = x$$ $$\implies x = 27$$
$$\implies \Delta x = 63-54 = 9$$
$$\implies\boxed{\text{You are 27, I am 18}}$$
So there seems to be a miscalculation by your teacher. (Obviously the reasoning is instructive but just to confirm, $9$ years ago you were $18$ and I was $9$, hence satisfying the first statement, and in $9$ years you will be $36$ and I will be $27$ meaning our ages will indeed sum to $63$)
A: 
My age was twice your age, when I was the same age as yours now. [...]

a - x = 2 (b - x)  ←  a - x = b

x is some years ago
a is my current age
b is your current age


[...] And when you are the same age as mine now, the sum of our ages is 63.

a = b + y  →  a + y + b + y = 63

y is some years from now

Solve a system with four equations and four variables; solution should be unique.
System solution (spoiler):

 a = 27, b = 18, x = 9, y = 9

 Source: https://www.mathportal.org/calculators/system-of-equations-solver/system-4x4.php using matrix: [1, -2, 1, 0; 1, -1, -1, 0; 1, -1, 0, -1; 1, 1, 0, 2;] at the LHS of the equation and vector column [0; 0; 0; 63;] at the RHS of the equation.

