Jerry had some action figures on a shelf in his room. Later he added 7 more action figures to the shelf. If there are a total of 10 action figures on his shelf now how many action figures did he have initially on the shelf?
Let's say that Jerry had $x$ action figures on the shelf. Later he added $y$ more, so the total number of action figures is:
$$
x + y = 10 \quad \Rightarrow \quad y = 10 - x
$$
Now we have two equations with two unknowns:
$$
x + y = 10 \quad \Rightarrow \quad y = 10 - x
$$
These equations are called linear equations. The solution of a linear equation is the value of the variable that satisfies the equation. In our case, this is the value of $x$ that satisfies both equations. 
$$
x + y = 10 \quad \Rightarrow \quad y = 10 - x \quad \Rightarrow \quad x + (10 - x) = 10
$$
$$
x + 10 - x = 10
$$
$$
2x = 10
$$
$$
x = 5
$$
Therefore, Jerry initially had $5$ action figures on the shelf. 