Question

Consider the following system of equations:

−x+y=5

y=(x−3)2+2

A. Is (1, 6) a solution to the system of equations? Support your answer by showing the algebraic steps of evaluating each equation with the potential solution.

(2 points)
0 / 10000 Word Limit
Question 2
B.. Graph the system of equations in GeoGebra to discover if there is a second solution. On the graph, label the solution(s) to the system of equations.

Upload a picture or screenshot of your labeled Geogebra graph.

In Geogebra the top left menu options include downloading to PDF which will work in this dropbox

Answer 1

### Question 1 - Part A:

To determine if the point (1, 6) is a solution to the system of equations, we need to evaluate both equations with \( x = 1 \) and \( y = 6 \).

#### First Equation:
The first equation is:
\[
-x + y = 5
\]
Substituting \( x = 1 \) and \( y = 6 \):
\[
-1 + 6 = 5
\]
Calculating the left side:
\[
5 = 5
\]
Thus, the first equation holds true.

#### Second Equation:
The second equation is:
\[
y = (x - 3)^2 + 2
\]
Again substituting \( x = 1 \) and \( y = 6 \):
\[
6 = (1 - 3)^2 + 2
\]
Calculating the right side:
\[
6 = (-2)^2 + 2
\]
\[
6 = 4 + 2
\]
\[
6 = 6
\]
Thus, the second equation also holds true.

### Conclusion for Part A:
Since both equations are satisfied with the point (1, 6), it is indeed a solution to the system of equations.

---

### Question 2 - Part B:

To graph the system of equations in GeoGebra, follow these steps:

1. **Open GeoGebra** and select the "Graphing" option.
2. **Input the equations** one at a time:
- For the first equation \( -x + y = 5 \):
- Type in: `y = x + 5`
- For the second equation \( y = (x - 3)^2 + 2 \):
- Type in: `y = (x - 3)^2 + 2`

3. **Graph the equations** and look for intersection points.
4. **Label the intersection points** on the graph.

**Uploading the Graph:**
Once you have completed the graphing and labeling, use the "File" menu in GeoGebra to download the graph as a PDF or image. Then, upload that file to your assignment dropbox.

If you need any additional help with using GeoGebra or further explanation, feel free to ask!