Question: Solve using substitution.
y = 9x - 9
y = 5x - 1
1. **State the problem:** We need to solve the system of equations using substitution:
$$y = 9x - 9$$
$$y = 5x - 1$$
2. **Use substitution method:** Since both expressions equal $y$, set them equal to each other:
$$9x - 9 = 5x - 1$$
3. **Solve for $x$:**
Subtract $5x$ from both sides:
$$9x - \cancel{5x} - 9 = \cancel{5x} - 1 - 5x$$
which simplifies to:
$$4x - 9 = -1$$
Add $9$ to both sides:
$$4x - 9 + 9 = -1 + 9$$
$$4x = 8$$
Divide both sides by $4$:
$$\frac{4x}{\cancel{4}} = \frac{8}{\cancel{4}}$$
$$x = 2$$
4. **Find $y$ by substituting $x=2$ into one of the original equations:**
Using $y = 9x - 9$:
$$y = 9(2) - 9 = 18 - 9 = 9$$
5. **Solution:**
The solution to the system is:
$$(x, y) = (2, 9)$$