The document provides step-by-step instructions for solving a system of equations modeling an arch and line intersecting in a sculpture. It gives the equations, shows how to isolate and set them equal to each other, solve for x, plug back into the original equations to solve for y, and write the solutions. It then provides an example problem of finding where a meteorite's trajectory intersects an air balloon's path, modeled by equations, and the solutions to some quiz problems.

1. Non-Linear Systems
Mr. Collado

2. Problem
An artist is building a sculpture and is using graph
paper to graph the sculpture. The monument
consists of an arch and a straight line. The
equations of the arch and the line are below. Find
the intersections of the arch and line.

3. Step 1: Isolate y
Since y is already isolated in both equations we
can move onto Step 2.

4. Step 2: Set the equations equal to each other
Since both equations are equal to y we can set
them equal to each other like this:

5. Step 3: Get all terms to one side
Move all the terms to one side by using inverse
operations like this:

6. Step 4: Factor out the perfect square trinomial
You can use either the box method, completing
the square, or the quadratic formula. For this
example, I am going to use the box method.

7. Step 4: (cont’d)
a = 1
b = -4
c = -12
ac = -12 b = -4
2 * -6 = -12 2 + (-6) = -4

8. Step 4: (cont’d)
(x-6)(x+2) = 0
x - 6 = 0 x + 2 = 0
x = 6 x = -2

9. Step 5: Plug in x to find y
Find the other half of the ordered by plugging in
the x-values into the original equations. I will use
this equation:

10. Step 6: Write the solutions
The solutions are:

11. Try this!
A meteorite was falling from the sky and an air
balloon with a camera was traveling to try to take
pictures of it. Their trajectories are modeled by the
following equations. Where do their trajectories
intersect?

12. Try this Solutions
The solutions are (1,2) and (2,1).

13. Quiz
Find the solutions to these equations:

14. Quiz Solutions
1. (-2, 2), (2.408, 2.9)
2. (-1, 0), (1, 0)