Question

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

$\left\{\begin{array}{l}y=\frac{3}{2}x+3\\ y=-x^2+2\end{array}\right.$

Short answer

There is no solution to this system of equations.

Step-by-step solution

Step 1. Given Information

The given system of equations is

$\left\{\begin{array}{l}y=\frac{3}{2}x+3\\ y=-x^2+2\end{array}\right.$.

Step 2. Graph the Equations

• Plot the graphs of 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 functions do not intersect.
• So, there is no solution to this system of equations.