The problem asks to solve the given system of equations by graphing:

$y = -x^2 + 4x + 5$ $y = 4x + 5$

Steps to Solve:

1. Graph the equations on the same coordinate plane:

   • The first equation, $y = -x^2 + 4x + 5$, is a quadratic equation representing a parabola.
   • The second equation, $y = 4x + 5$, is a linear equation representing a straight line.

2. Identify points of intersection:

   • The points where the parabola and line intersect represent the solutions to the system of equations.

3. Solve algebraically (optional for confirmation): Substitute $y = 4x + 5$ into $y = -x^2 + 4x + 5$ to find the x-values of the intersection points.

Algebraic Solution:

Substitute $y = 4x + 5$ into $y = -x^2 + 4x + 5$: $4x + 5 = -x^2 + 4x + 5$ Simplify: $0 = -x^2$ $x = 0$

Plotting