Question

solve the system of equations by graphing. first graph the equations, and then identify the solutions.
( y = -2x + 5 )
( y = x^2 - 6x + 8 )
to graph a linear equation, click to plot points on the graph. to graph a quadratic equation, click to plot the vertex first, then plot another point on the graph.

Explanation:

Step1: Set equations equal

To find solutions, set $-2x + 5 = x^2 - 6x + 8$.

Step2: Rearrange to quadratic

Rearrange: $x^2 - 4x + 3 = 0$.

Step3: Factor the quadratic

Factor: $(x - 1)(x - 3) = 0$.

Step4: Solve for x

Solve: $x = 1$ or $x = 3$.

Step5: Find corresponding y

For $x = 1$, $y = -2(1) + 5 = 3$. For $x = 3$, $y = -2(3) + 5 = -1$.

Answer:

The solutions are $(1, 3)$ and $(3, -1)$.