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 the equations equal

To find the solutions, set \(-2x + 5 = x^2 - 6x + 9\).

Step2: Rearrange into standard quadratic form

Rearrange the equation: \(x^2 - 6x + 9 + 2x - 5 = 0\) simplifies to \(x^2 - 4x + 4 = 0\).

Step3: Factor the quadratic

Factor the quadratic: \((x - 2)^2 = 0\).

Step4: Solve for x

Solve for \(x\): \(x - 2 = 0\) gives \(x = 2\).

Step5: Find the corresponding y - value

Substitute \(x = 2\) into \(y = -2x + 5\): \(y=-2(2)+5 = 1\).

Answer:

The solution to the system of equations is \((2,1)\)