Given x = 2 and y = x times x, find the value of y.

Step-by-step solution

1. 1

   Identify which equation defines what. The first equation fixes the value of $x$; the second defines $y$ in terms of $x$. So the order of work is forced: use the known $x$ to compute the unknown $y$.

2. 2

   Recognise the expression. $x\cdot x$ is $x$ multiplied by itself, which is $x^2$ — the square of $x$. It is not $2x$: multiplying by itself and doubling are different operations, and they happen to agree only at $x=0$ and $x=2$.

3. 3

   Substitute the known value. Replace every $x$ in the second equation with $2$:

   $y=x\cdot x=2\cdot2$

4. 4

   Compute.

   $y=4$

5. 5

   Verify and note the coincidence. Squaring: $2^2=4$ ✓. Here doubling would also give $4$, because $2$ is one of the two fixed points of "square versus double" — a coincidence worth flagging, since at $x=3$ the two would differ ($9$ versus $6$). So this particular problem cannot distinguish the two readings, but $x\cdot x=x^2$ is the correct one.