Question

on the set of axes below, solve the following system of equations graphically and state the coordinates of all points in the solution set.

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

$y = -x + 2$

you can move the parabola by dragging the dots. graph the line by clicking twice.

Explanation:

Step1: Find intersection by solving equations

Set \(x^{2}-4x - 2=-x + 2\).
Rearrange to \(x^{2}-3x - 4 = 0\).
Factor: \((x - 4)(x+1)=0\).

Step2: Solve for x

\(x - 4 = 0\) gives \(x = 4\); \(x + 1 = 0\) gives \(x=-1\).

Step3: Find corresponding y

For \(x = 4\), \(y=-4 + 2=-2\).
For \(x=-1\), \(y=-(-1)+2 = 3\).

Answer:

The solution set is \(\{(-1, 3), (4, -2)\}\)