Question

y = -2x + 3; y = x² - 6x + 3 (graph with grid, axes, and two curves: a line and a parabola)

Explanation:

Step1: Identify the equations

We have a linear equation \( y = -2x + 3 \) and a quadratic equation \( y = x^2 - 6x + 3 \). To find the intersection points, we set them equal:
\( -2x + 3 = x^2 - 6x + 3 \)

Step2: Solve the equation

Simplify the equation:
\( x^2 - 6x + 3 + 2x - 3 = 0 \)
\( x^2 - 4x = 0 \)
Factor:
\( x(x - 4) = 0 \)
So \( x = 0 \) or \( x = 4 \)

Step3: Find corresponding y-values

For \( x = 0 \): \( y = -2(0) + 3 = 3 \)
For \( x = 4 \): \( y = -2(4) + 3 = -5 \)
So the intersection points are \( (0, 3) \) and \( (4, -5) \), which match the graph.

Answer:

The intersection points are \((0, 3)\) and \((4, -5)\) (or as per the graph's marked points, confirming the solutions to the system of equations \( y = -2x + 3 \) and \( y = x^2 - 6x + 3 \)).