Add the two equations term by term to eliminate one variable. What equation in terms of only $y$ do you get?

Once you know $y$, plug it back into either original equation (pick the simpler one) and solve for $x$.

After you get values for $x$ and $y$, substitute them into both original equations to be sure they satisfy each one before choosing from the answer options.

In Desmos, type the first equation solved for $y$, for example y = (x + 7)/2. This will graph the line that represents $2y - x = 7$.

On a new line, type the second equation solved for $y$, for example y = (13 - x)/3. This graphs the line that represents $3y + x = 13$.

Look for the point where the two lines intersect. Tap or click that intersection point; Desmos will display its coordinates $(x, y)$. Compare that ordered pair to the answer choices and select the matching one.

Notice that in the system

the $x$ terms have opposite signs ($-x$ and $+x$). This makes the elimination (addition) method very convenient, because adding the equations will cancel $x$.

Add the left sides and the right sides of the two equations:

Now solve $5y = 20$ for $y$ by dividing both sides by $5$ to find the value of $y$.

Take the $y$ value you just found and substitute it into one of the original equations, for example $2y - x = 7$.

1. Replace $y$ with its value and simplify the left side.
2. Solve the resulting simple equation for $x$.

This gives you the corresponding $x$ value.

Combine the values you found into an ordered pair $(x, y)$: $x = 1$ and $y = 4$, so the solution is $(1,4)$. This matches answer choice A.