Question

In the following exercises, solve the system of equations by using graphing.

$\begin{array}{rcl}& & \left\{\begin{array}{l}x=2\\ {(x+2)}^2+{(y+3)}^2=16\end{array}\right.\end{array}$

Short answer

The solution of the system is $(2,-3)$.

Step-by-step solution

Step 1. Given Information

The given system of equations is

$\begin{array}{rcl}& & \left\{\begin{array}{l}x=2\\ {(x+2)}^2+{(y+3)}^2=16\end{array}\right.\end{array}$

Step 2. Graph the equations

• Plot both the given equations on the same graph.

• The blue line represents the first equation and the red line represents the second equation of the system.

Step 3. Determine the point of intersection 

• From the graph, it is observed that the point of intersection of both equations is$(2,-3)$.
• So, the solution of the system is$(2,-3)$.