In the equation $2x + y = 13$, replace $y$ with the expression from the first equation. What new equation in terms of $x$ do you get?

After substitution, combine like terms and isolate $x$. What value of $x$ makes both sides of the equation equal?

Type y = 7 - x into Desmos as the first equation. Then type the second equation as either 2x + y = 13 or rewritten as y = -2x + 13 so that both graphs appear.

Look for the point where the two lines intersect. Click on the intersection point; Desmos will show its coordinates $(x, y)$. The $x$-coordinate of this point is the value you need for the question.

The first equation already gives $y$ in terms of $x$: $y = 7 - x$. Use substitution by replacing $y$ in the second equation, $2x + y = 13$, with $7 - x$.

After substitution, the second equation becomes:

Combine like terms on the left side:

Now solve $x + 7 = 13$:

So, the value of $x$ is $6$, which corresponds to choice C.