Solve the system by graphing. Check your solution
y=x
y=-x+4
create a line for each equation
To graph the first equation, y = x, we can assign different values to x and calculate the corresponding values of y. Here's a table of values:
| x | y |
|:---:|:---:|
| 0 | 0 |
| 1 | 1 |
| 2 | 2 |
| -1 | -1 |
| -2 | -2 |
Plotting these points on a graph and connecting them, we get a straight line passing through the origin (0,0) and with a slope of 1.
Next, let's graph the second equation, y = -x + 4, using the same process:
| x | y |
|:---:|:---:|
| 0 | 4 |
| 1 | 3 |
| 2 | 2 |
| -1 | 5 |
| -2 | 6 |
Plotting these points on the graph and connecting them, we get a straight line with an intercept at the y-axis (0,4) and a slope of -1.
Now, let's put both lines on the same graph:
Graph:
```
|
6 | *
| *
5 | *
| *
4 | * *
| *
3 |*
|
2 | * *
| *
1 | *
| *
0 |____________
0 1 2 3 4
```
The first line (y = x) is represented by dots forming a line with a positive slope, passing through the origin (0,0). The second line (y = -x + 4) is represented by dots forming a line with a negative slope, intersecting the y-axis at the point (0,4).
The solution to the system of equations is the point where both lines intersect, which is (2,2).
To check the solution, substitute the coordinates (2,2) into the original equations:
1) For y = x: 2 = 2. This is true.
2) For y = -x + 4: 2 = -(2) + 4. This is also true.
Therefore, the solution (2,2) satisfies both equations, and our solution is correct.