Question: Solve using substitution.
y = –7x − 8
y = –x + 4
1. **State the problem:** We need to solve the system of equations using substitution:
$$y = -7x - 8$$
$$y = -x + 4$$
2. **Use substitution method:** Since both equations equal $y$, set the right sides equal to each other:
$$-7x - 8 = -x + 4$$
3. **Solve for $x$:**
Add $7x$ to both sides:
$$-7x - 8 + 7x = -x + 4 + 7x$$
$$-8 = 6x + 4$$
Subtract $4$ from both sides:
$$-8 - 4 = 6x + 4 - 4$$
$$-12 = 6x$$
Divide both sides by $\cancel{6}$ to isolate $x$:
$$x = \frac{-12}{\cancel{6}}$$
$$x = -2$$
4. **Find $y$ by substituting $x = -2$ into one of the original equations:**
Using $y = -x + 4$:
$$y = -(-2) + 4$$
$$y = 2 + 4$$
$$y = 6$$
5. **Solution:** The solution to the system is:
$$(x, y) = (-2, 6)$$