Question: Solve using substitution.
y = 4x + 2
y = 9x - 8
1. **State the problem:** We need to solve the system of equations using substitution:
$$y = 4x + 2$$
$$y = 9x - 8$$
2. **Use substitution method:** Since both expressions equal $y$, set them equal to each other:
$$4x + 2 = 9x - 8$$
3. **Solve for $x$:**
Subtract $4x$ from both sides:
$$\cancel{4x} + 2 = 9x - \cancel{4x} - 8 \implies 2 = 5x - 8$$
Add $8$ to both sides:
$$2 + 8 = 5x - 8 + 8 \implies 10 = 5x$$
Divide both sides by $5$:
$$\frac{10}{\cancel{5}} = \frac{5x}{\cancel{5}} \implies 2 = x$$
4. **Find $y$ by substituting $x=2$ into one of the original equations:**
Using $y = 4x + 2$:
$$y = 4(2) + 2 = 8 + 2 = 10$$
5. **Solution:** The solution to the system is:
$$(x, y) = (2, 10)$$