To solve the system of equations y = x + 2 and y = 2x + 7, you can use either graphing or creating a table of values. Here’s how to do both:
Method 1: Graphing
1. **Graph the first equation**: For the equation y = x + 2, you can easily find two points. For example:
- If x = 0, then y = 0 + 2 = 2 (Point: (0, 2))
- If x = 2, then y = 2 + 2 = 4 (Point: (2, 4))
Plot these points on a graph and draw a straight line through them.
2. **Graph the second equation**: For the equation y = 2x + 7, find two more points:
- If x = 0, then y = 2(0) + 7 = 7 (Point: (0, 7))
- If x = 1, then y = 2(1) + 7 = 9 (Point: (1, 9))
Plot these points and draw a line through them as well.
3. **Find the intersection**: The solution to the system of equations is the point where the two lines intersect. In this case, the lines will intersect at a certain point, which represents the values of x and y that satisfy both equations.
Method 2: Using a Table
1. **Create a table for the first equation**: Choose some values for x and find corresponding y values:
| x | y = x + 2 |
|---|---|
| 0 | 2 |
| 1 | 3 |
| 2 | 4 |
| 3 | 5 |
2. **Create a table for the second equation**: Similarly, create a table for y = 2x + 7:
| x | y = 2x + 7 |
|---|---|
| 0 | 7 |
| 1 | 9 |
| 2 | 11 |
| 3 | 13 |
3. **Analyze the tables**: Compare the y values from both tables to find a common point. This will help you see the values of x and y that satisfy both equations.
Once you have either method worked out, you’ll find the solution to the system of equations! Remember, the lines represent all the possible solutions, but the intersection is the specific solution to the system.