https://file.aiquickdraw.com/mathbot/file/1731946179940734yblry.jpg

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

Solve the system of equations by graphing: y = -x^2 + 4x + 5 and y = 4x + 5.

Learn how to solve a system of equations involving a quadratic equation y = -x^2 + 4x + 5 and a linear equation y = 4x + 5 by graphing. Explore key algebraic concepts and find intersection points for solutions. Suitable for Grades 8-10.

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