To graph the system, we need to plot the two equations on a graph and see where they intersect.
First, let's graph the equation y = -x + 7:
To do this, we need to find a few points that lie on the line. We can do this by substituting different values of x into the equation and solving for y.
When x = 0, y = -0 + 7 = 7. This gives us the point (0, 7).
When x = 2, y = -2 + 7 = 5. This gives us the point (2, 5).
When x = -3, y = -(-3) + 7 = 10. This gives us the point (-3, 10).
Plotting these points, we can draw a straight line through them:
```
|
10| x
| |
| |
| x |
| x |
| x |
| |
| x |
|______________________________ x__,0_______
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
```
Next, let's graph the equation y = x + 1:
Following the same process as before, we find the following points:
When x = 0, y = 0 + 1 = 1. This gives us the point (0, 1).
When x = 2, y = 2 + 1 = 3. This gives us the point (2, 3).
When x = -3, y = -3 + 1 = -2. This gives us the point (-3, -2).
Plotting these points, we can draw a straight line through them:
```
|
10| x
| |
| |
| x |
| x |
| x |
| x |
| x |
|______________________________ x__,0_______
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
```
Now, we can see that the two lines intersect at the point (3, 4). Therefore, the solution to the system is x = 3 and y = 4.
To check the solution, we substitute these values into the two equations:
For the first equation, y = -x + 7:
4 = -3 + 7
4 = 4
For the second equation, y = x + 1:
4 = 3 + 1
4 = 4
Both equations are satisfied, so the solution is correct.
Solve the system by graphing. Check your solution.
y = -x + 7
y = x + 1
1 answer
1 answer