Consider adding or subtracting the two equations. Which operation (addition or subtraction) might give you an expression that looks related to $x+2y$?

If you can create an equation involving $2x+4y$, remember that $2x+4y = 2(x+2y)$. How can you get $2x+4y$ from the two given equations?

Rewrite each equation in slope-intercept form and enter them into Desmos:

• For $3x+2y=34$, type y = (34 - 3x)/2.
• For $x-2y=2$, type y = (x - 2)/2.

You will see two lines on the graph.

Click on the point where the two lines intersect. Desmos will show the coordinates of this point; these are the values of $x$ and $y$ that satisfy the system.

Using the $x$- and $y$-coordinates from the intersection, type a new expression in Desmos of the form x_value + 2*y_value (replacing x_value and y_value with the numbers from the intersection). The output of this expression is the value of $x+2y$.

You are asked for $x+2y$, not for $x$ and $y$ separately. Notice that if you knew $2x+4y$, then $x+2y$ would just be half of that, because $2(x+2y)=2x+4y$.

Start with the given system:

Subtract the second equation from the first:

Be careful with the minus sign:

• Left side:

• Right side:

So you get the new equation:

From the previous step, you have $2x + 4y = 32$. This is the same as $2(x+2y)$, so:

Divide both sides by 2:

So the value of $x + 2y$ is 16, which corresponds to choice C.