To solve the system of equations, we start with the two equations:
- Equation 1: y = 2x + 8
- Equation 2: y = x + 4
Since both equations are equal to y, we can set them equal to each other:
2x + 8 = x + 4
Now, we can solve for x. First, subtract x from both sides:
2x – x + 8 = 4
x + 8 = 4
Next, subtract 8 from both sides:
x = 4 – 8
x = -4
Now that we have the value of x, we can substitute it back into one of the original equations to find y. We can use Equation 2:
y = x + 4
y = -4 + 4
y = 0
Thus, the solution to the system of equations is:
(x, y) = (-4, 0)
This means the two lines represented by the equations intersect at the point (-4, 0).