Question

which represents the solution(s) of the graphed system of equations, $y = x^2 + 2x - 3$ and $y = x - 1$?

Explanation:

Step1: Recall solution of system

The solution of a system of equations graphed is the point(s) of intersection of the graphs.

Step2: Identify intersection points

Looking at the graph, the blue parabola (\(y = x^2 + 2x - 3\)) and the red line (\(y = x - 1\)) intersect at two points. By observing the coordinates:

• One intersection is at \(x = -2\), substitute into \(y = x - 1\), \(y = -2 - 1 = -3\), so \((-2, -3)\).
• The other intersection is at \(x = 1\), substitute into \(y = x - 1\), \(y = 1 - 1 = 0\), so \((1, 0)\).

Answer:

The solutions are \((-2, -3)\) and \((1, 0)\)