Once you have $y$ as an expression involving $x$, plug that expression into the equation $xy = 6$. This should give you an equation that only has $x$.

After substituting, you should get a quadratic equation in $x$. Rearrange it into the form $ax^2 + bx + c = 0$ and then factor it.

You will get two possible values for $x$ from the quadratic. Look at the answer choices and see which of your solutions appears there.

In Desmos, type y = 5 - x for the first equation and y = 6/x for the second equation. These represent all $(x, y)$ pairs that satisfy each equation.

Look at where the two graphs intersect. Click each intersection point and note the $x$-coordinates. Compare these $x$-values to the answer choices and see which choice matches one of them.

From the first equation, $x + y = 5$, solve for $y$:

Now you have $y$ written in terms of $x$.

Use the expression for $y$ in the second equation $xy = 6$.

Substitute $y = 5 - x$:

Now the equation has only $x$.

Distribute $x$ on the left side:

Move all terms to one side to set the equation equal to 0:

Multiply both sides by $-1$ (which does not change the solutions):

This is a quadratic equation in standard form.

Factor the quadratic:

So the possible $x$-values that satisfy the system are $x = 2$ and $x = 3$.

Check the answer choices $1, 2, 4, 6$: the only choice that matches one of these values is 2, so the correct answer is choice B.