Once you know the value of $y$, substitute that value into the other equation $y=-2x+5$ to create an equation with only $x$.

When you solve the equation for $x$, make sure you correctly add or subtract on both sides and then divide, paying attention to negative signs.

In a new line in Desmos, type y = -2x + 5 to graph the first line.

In another line, type y = -1 to graph the horizontal line from the second equation.

Look for the point where the two lines cross. Click on the intersection; Desmos will display its coordinates. The $x$- and $y$-values of this intersection give the solution to the system.

Look at the second equation:

This tells you immediately that in the solution to the system, the $y$-value must be $-1$.

Now take $y=-1$ and plug it into the first equation $y=-2x+5$.

Replace $y$ with $-1$:

Now you have an equation with only $x$.

Solve $-1 = -2x + 5$ step by step:

• Subtract 5 from both sides:

• Divide both sides by $-2$:

So the $x$-value of the solution is $3$.

You found that $x=3$ and earlier that $y=-1$.

So the solution to the system is the ordered pair $(3,-1)$.

Quick check:

• First equation: $y=-2x+5$ becomes $-1 = -2(3) + 5 = -6 + 5 = -1$ (true).
• Second equation: $y=-1$ is clearly satisfied by $y=-1$.

Since the point satisfies both equations, $(3,-1)$ is correct.