The image shows two functions: a blue parabola and a red straight line. To identify the system of equations, I will analyze the key characteristics of both graphs.

1. Parabola (blue graph):

   • The parabola opens downwards, suggesting it has a negative leading coefficient.
   • The vertex appears to be at $(0, 2)$.
   • The parabola crosses the x-axis near $x = -3$ and $x = 3$, which could be roots.
   • A possible equation for this parabola is in the form:
     $y = a(x - h)^2 + k$ where $(h, k)$ is the vertex. Here, $(h, k) = (0, 2)$, so the equation might be: $y = a(x - 0)^2 + 2 = ax^2 + 2$ Given that the parabola opens downwards, $a$ is negative. Using approximate values for the x-intercepts at $x = -3$ and $x = 3$, we can estimate: $y = -\frac{2}{9}x^2 + 2$ as the equation of the parabola.

2. Line (red graph):

   • The line has a positive slope and crosses the y-axis around $y = -1$.
   • It crosses the x-axis at approximately $x = -1.5$ and the y-axis at $y = -1$.
   • Using the slope-intercept form $y = mx + b$, where $b$ is the y-intercept and $m$ is the slope, we estimate the slope $m$ as: $m = \frac{3 - (-1)}{4 - 0} = \frac{4}{4} = 1$ So, the line equation is approximately: $y = x - 1$

System of equations: