Question: Solve using substitution.
y = 3x + 4
y = 4x + 8
1. **State the problem:** We need to solve the system of equations using substitution:
$$y = 3x + 4$$
$$y = 4x + 8$$
2. **Use substitution method:** Since both equations equal $y$, set them equal to each other:
$$3x + 4 = 4x + 8$$
3. **Solve for $x$:**
Subtract $3x$ from both sides:
$$\cancel{3x} + 4 = \cancel{3x} + 4x + 8 - 3x$$
which simplifies to:
$$4 = x + 8$$
Subtract $8$ from both sides:
$$4 - 8 = x + 8 - 8$$
$$-4 = x$$
4. **Find $y$ by substituting $x = -4$ into one of the original equations:**
Using $y = 3x + 4$:
$$y = 3(-4) + 4 = -12 + 4 = -8$$
5. **Final solution:**
$$x = -4, \quad y = -8$$
This is the point where the two lines intersect.