Notice that one equation has $-y$ and the other has $+y$. What happens if you add the two equations together?

Once you get an equation with only $x$, solve it, then substitute that value back into one of the original equations to find $y$.

After you know $x$ and $y$, carefully plug them into $x + 2y$. Be sure to multiply $2$ by $y$ before adding $x$.

In Desmos, enter the two equations in slope-intercept form:

• Type y = 3x - 7 on one line.
• Type y = 5 - x on another line. Desmos will graph both lines.

Click on the point where the two lines intersect. Desmos will display the coordinates of this intersection as $(a, b)$, which represent the solution $(x, y)$ of the system.

In a new expression line, type the x-coordinate of the intersection plus 2 times the y-coordinate. For example, if the intersection were $(a, b)$, you would type a + 2*b using the actual numbers from the point. The value Desmos displays is the value of $x + 2y$; choose the answer option that matches this value.

Start with the system:

Add the two equations together. When you add them, the $-y$ and $+y$ terms cancel out:

This simplifies to an equation in just $x$.

From adding the equations you get:

Combine like terms:

Now divide both sides by 4 to find the value of $x$.

Take the value of $x$ you just found and substitute it into the simpler equation $x + y = 5$:

Replace $x$ with the number you found, then solve the resulting equation to get $y$.

Now that you know both $x$ and $y$, plug them into $x + 2y$:

So $x + 2y = 7$, which corresponds to choice D.