After you eliminate one variable, you will get a simple equation in terms of the other variable. Solve that equation first.

Once you find one variable, plug it into either original equation to find the other variable, and then make sure your ordered pair works in both equations.

Rewrite each equation in $y$-form, then type them into Desmos as separate lines: $y = 7 - 3x$ and $y = x - 1$. This will graph two straight lines.

On the graph, locate the point where the two lines cross. Tap or click that intersection; Desmos will display its coordinates. Those coordinates give you the $(x, y)$ solution to the system.

Add the two equations to eliminate $y$:

• First equation: $3x + y = 7$
• Second equation: $x - y = 1$

When you add them, the $y$ terms cancel:

Now you have a simple equation with just $x$.

Solve $4x = 8$:

So the $x$-coordinate of the solution is $2$.

Use either original equation to find $y$. Using $x - y = 1$:

Subtract $2$ from both sides:

Multiply both sides by $-1$:

So the $y$-coordinate of the solution is $1$.

The solution to the system is the ordered pair $(x, y)$ with $x = 2$ and $y = 1$, so the solution is $(2, 1)$.

Quick check in both equations:

• First equation: $3(2) + 1 = 6 + 1 = 7$ ✓
• Second equation: $2 - 1 = 1$ ✓

Since $(2, 1)$ satisfies both equations, it is the correct solution.