We can find the solution to a system of equations by graphing the equations. Let's do this with the following systems of equations:

First, let's graph the first equation $\goldD{y=\dfrac{1}{2}x+3}$. Notice that the equation is already in $y$-intercept form so we can graph it by starting at the $y$-intercept of $3$, and then going up $1$ and to the right $2$ from there.

Next, let's graph the second equation $\greenE{y=x+1}$ as well.

There is exactly one point where the graphs intersect. This is the solution to the system of equations.

This makes sense because every point on the gold line is a solution to the equation $\goldD{y=\dfrac{1}{2}x+3}$, and every point on the green line is a solution to $\greenE{y=x+1}$. So, the only point that's

**a solution to both equations**is the point of intersection## Checking the solution

So, from graphing the two equations, we found that the ordered pair $(4,5)$ is the solution to the system. Let's verify this by plugging $x =4$ and $y = 5$ into each equation.

The first equation:

The second equation:

Nice! $(4, 5)$ is indeed a solution.