Systems of equations with graphing

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 $y={\displaystyle \frac{1}{2}}x+3$‍. 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 $y=x+1$‍ 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 $y={\displaystyle \frac{1}{2}}x+3$‍, and every point on the green line is a solution to $y=x+1$‍. So, the only point that's a solution to both equations is the point of intersection

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.