After you add the equations, you should get an equation with only $x$. Solve that equation to find $x$.

Plug the value of $x$ into one of the original equations to find $y$, then add $x$ and $y$.

In Desmos, enter the two equations as separate lines:

• 2x + y = 11
• x - y = 1

Look at the graph and identify the point where the two lines intersect. This point gives you the solution $(x, y)$ to the system.

In a new expression line, type the x-coordinate of the intersection plus the y-coordinate (for example, if the intersection is $(a, b)$, type a + b). The value Desmos shows for this sum is the required value of $x + y$.

We are given the system

and we are asked to find the value of $x + y$ for the solution $(x, y)$ that satisfies both equations.

Notice that the $y$ terms have opposite signs ($+y$ and $-y$), so adding the two equations will eliminate $y$:

• Add left sides: $(2x + y) + (x - y) = 3x$
• Add right sides: $11 + 1 = 12$

So we get

Solve for $x$ by dividing both sides by $3$.

From $3x = 12$, we have $x = 4$.

Now substitute $x = 4$ into either original equation. Using $x - y = 1$:

Subtract $1$ from both sides or solve directly to find $y$.

From $4 - y = 1$, subtract $1$ from both sides to get $3 = y$, so $y = 3$.

Now compute $x + y$:

So the value of $x + y$ is $7$, which corresponds to choice C.