Try adding the two equations together. What happens to the coefficients of $x$ and $y$ when you do that?

After you add the equations, see if you can factor something out so that the expression $x + y$ appears.

Once you have an equation with $x + y$, use basic algebra to get $x + y$ alone on one side.

In Desmos, type 3x + 7y = 68 on one line and 7x + 3y = 52 on the next line. Desmos will graph both lines.

Click on the point where the two lines intersect. Desmos will display the coordinates of this point as $(x, y)$ in decimal or exact form.

Use the displayed $x$ and $y$ values from the intersection point and either mentally add them or type an expression in Desmos with those numbers to find $x + y$.

Add the left and right sides of the two equations:

On the left, combine like terms: $3x + 7x = 10x$ and $7y + 3y = 10y$, so the left side becomes $10x + 10y$.

On the right, add $68 + 52 = 120$.

So you get:

Both terms on the left side have a factor of $10$, so factor it out:

This gives:

Now solve for $x + y$ by dividing both sides by $10$:

So the value of $x + y$ is 12.