Question

When the system of equations y + 2 = (x − 4)2

and
2x + y − 6 = 0 is solved graphically, the solution is
1) (−4, −2) and (−2, 2)
2) (4, −2) and (2, 2)
3) (−4, 2) and (−6, 6)
4) (4, 2) and (6, 6)

Answer 1

When solving a system of equations graphically, we find the points where the two equations intersect on a graph. These points represent the solutions to the system of equations.

To solve the given system of equations:

1) y + 2 = (x − 4)^2

2) 2x + y − 6 = 0

We can start by graphing both equations on the same coordinate plane.

The first equation, y + 2 = (x − 4)^2, is a quadratic equation. It represents a parabola. By rearranging the equation, we get y = (x − 4)^2 - 2. This equation tells us that for each x-coordinate, we can find the corresponding y-coordinate by substituting the x-value into the equation.

The second equation, 2x + y − 6 = 0, is a linear equation. It represents a straight line. By rearranging the equation, we get y = -2x + 6. This equation tells us that for each x-coordinate, we can find the corresponding y-coordinate by substituting the x-value into the equation.

Now, we can graph both equations on the same coordinate plane and find the points where they intersect. The points of intersection are the solutions to the system of equations.

After graphing the equations, it appears that the points of intersection are approximately (4, -2) and (2, 2).

Therefore, the correct answer is option 2) (4, -2) and (2, 2).

Explanation: