After you add the equations, you should get an equation with only $x$. Solve that equation to find the value of $x$.

Once you know $x$, plug it back into either $x + y = 8$ or $x - y = 2$ to find $y$.

For any answer choice you consider, plug its $x$ and $y$ into both equations and see if both equations come out true.

Rewrite $x + y = 8$ as $y = 8 - x$ and $x - y = 2$ as $y = x - 2$ so they can be graphed easily.

In Desmos, enter y = 8 - x and on a new line enter y = x - 2. Look for the point where the two lines intersect.

Click or tap the intersection point of the two lines. The coordinates shown are the $(x, y)$ pair that solves the system of equations.

The system is

If you add the left sides and the right sides, the $+y$ and $-y$ terms cancel:

This simplifies to

From $2x = 10$, divide both sides by $2$:

Now you know the value of $x$.

Substitute $x = 5$ into either original equation, for example $x + y = 8$:

Subtract $5$ from both sides:

Now you know both $x$ and $y$.

The solution to the system is the ordered pair $(x, y)$ using the values you found: $(5, 3)$.

Check quickly:

• First equation: $5 + 3 = 8$ ✓
• Second equation: $5 - 3 = 2$ ✓

Since this pair makes both equations true, $(5, 3)$ is the correct solution.