How can we solve the system of equations y = 2x + 8 and y = x + 4?

To solve the system of equations y = 2x + 8 and y = x + 4, we can use the substitution method since both equations are already set to y.

1. **Set the two equations equal to each other:**

Since both expressions equal y, we can set them equal to each other:

2x + 8 = x + 4

2. **Solve for x:**

Now, let’s isolate x:

2x + 8 = x + 4

2x - x = 4 - 8

x = -4

3. **Substitute x back into one of the original equations to find y:**

We can use either equation for this. Let’s use y = x + 4:

y = -4 + 4

y = 0

4. **Conclusion – The solution of the system of equations:**

The solution to the system of equations is the point (-4, 0). This means that the two lines represented by these equations intersect at the point (-4, 0).

5. **Graphical Representation:**

If you were to graph the equations y = 2x + 8 and y = x + 4, you would see two lines that intersect at the point (-4, 0). This visual confirms our solution and shows how both lines represent the same solution in two dimensions.