Look at the two equations and choose the one that is easier to solve for one variable. In this case, it is simple to solve $5x + y = 1$ for y.

Once you express y in terms of x from the second equation, substitute that expression into the first equation to find x. Then plug that x-value back into one of the original equations to find y.

After you know the numerical values of x and y, remember that $a = x$ and $b = y$. Add those two numbers to get $a + b$.

In Desmos, enter the two equations on separate lines exactly as they appear: 3x - 2y = 7 and 5x + y = 1. Desmos will draw two lines.

Click on the point where the two lines intersect. Desmos will show the coordinates of this point, which are the values of a (the x-coordinate) and b (the y-coordinate).

In a new expression line, type the x-coordinate plus the y-coordinate of the intersection point (for example, if the point is (p, q), type p + q). The value Desmos displays is the value of $a + b$.

We are given a system of two linear equations in x and y:

We are told that the solution to this system is the ordered pair (a, b). That means a = x and b = y at the intersection of the two lines. The question asks for $a + b$, which is the same as $x + y$ for the solution of the system.

Use the second equation because it is easy to solve for y:

Subtract 5x from both sides:

Now you have y written in terms of x.

Substitute $y = 1 - 5x$ into the first equation $3x - 2y = 7$:

Distribute the -2:

Combine like terms:

Add 2 to both sides:

Divide both sides by 13:

Now plug $x = 9/13$ into $y = 1 - 5x$:

First compute $5(9/13) = 45/13$. Rewrite 1 as $13/13$:

Subtract the numerators:

So the solution to the system is $x = 9/13$ and $y = -32/13$, which means $a = 9/13$ and $b = -32/13$.

We want $a + b$, which is the same as $x + y$ at the solution:

Combine the fractions by adding the numerators:

So the value of $a + b$ is $-23/13$, which corresponds to choice D.