Here is a system of equations.
y=2x+5
y=x+3
Graph the system. Then write its solution. Note that you can also answer "No solution" or "Infinitely many" solutions.
To graph the system, we can plot the two equations on a graph.
The first equation, y=2x+5, has a y-intercept of 5 and a slope of 2. This means that for every increase of 1 unit in x, y increases by 2 units. We can plot a few points to sketch the line:
For x=0, y=5. This gives us the point (0,5).
For x=1, y=7. This gives us the point (1,7).
For x=-1, y=3. This gives us the point (-1,3).
The second equation, y=x+3, also has a y-intercept of 3 and a slope of 1. Again, we can plot a few points to sketch the line:
For x=0, y=3. This gives us the point (0,3).
For x=1, y=4. This gives us the point (1,4).
For x=-1, y=2. This gives us the point (-1,2).
Now, let's plot these points on a graph:
```
|
7 | .
|
6 |
|
5 | *
|
4 | .
|
3 | *
|
2 | .
|___
-2 -1 0 1 2 3 4 5 6
```
The lines intersect at the point (-1,2). Therefore, the solution to the system of equations is x=-1 and y=2.