14. (7-2) Solve the system using substitution. 15. (7-4) Solve the system using elimination. $$ \begin{array}{c}4 x+3 y=-2 \ x+5 y=-9 \ 3 x+3 y=-15 \ 5 x-9 y=3\end{array} $$

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## **Problem 14. (7-2) Solve the system using substitution.**

**Given System:**
$$
\begin{cases}
4x + 3y = -2 & \text{(1)} \
x + 5y = -9 & \text{(2)}
\end{cases}
$$

**Step 1: Solve one equation for one variable.**

Let's solve equation (2) for $$ x $$:
$$
x + 5y = -9 \
\Rightarrow x = -9 - 5y \quad \text{(3)}
$$

**Step 2: Substitute this expression into the other equation.**

Substitute $$ x = -9 - 5y $$ into equation (1):
$$
4(-9 - 5y) + 3y = -2 \
-36 - 20y + 3y = -2 \
-36 - 17y = -2
$$

**Step 3: Solve for $$ y $$.**
$$
-17y = -2 + 36 \
-17y = 34 \
y = \frac{34}{-17} \
y = -2
$$

**Step 4: Substitute $$ y $$ back into equation (3) to find $$ x $$.**
$$
x = -9 - 5(-2) \
x = -9 + 10 \
x = 1
$$

**Solution:**
$$
x = 1,\quad y = -2
$$

---

## **Problem 15. (7-4) Solve the system using elimination.**

**Given System:**
$$
\begin{cases}
3x + 3y = -15 & \text{(1)} \
5x - 9y = 3 & \text{(2)}
\end{cases}
$$

**Step 1: Simplify the equations if possible.**

Divide equation (1) by 3:
$$
3x + 3y = -15 \
\Rightarrow x + y = -5 \quad \text{(3)}
$$

**Step 2: Align the equations for elimination.**

From equation (3):
$$
x + y = -5
$$
Multiply equation (3) by 9 to align the coefficients of $$ y $$ with equation (2):
$$
9x + 9y = -45 \quad \text{(4)}
$$

Now, write equation (2):
$$
5x - 9y = 3 \quad \text{(2)}
$$

**Step 3: Add equations (4) and (2) to eliminate $$ y $$.**
$$
9x + 9y + 5x - 9y = -45 + 3 \
14x = -42 \
x = \frac{-42}{14} \
x = -3
$$

**Step 4: Substitute $$ x = -3 $$ back into equation (3) to find $$ y $$.**
$$
-3 + y = -5 \
y = -5 + 3 \
y = -2
$$

**Solution:**
$$
x = -3,\quad y = -2
$$

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**Final Summary:**

- **Problem 14 Solution:** $$ x = 1 $$, $$ y = -2 $$
- **Problem 15 Solution:** $$ x = -3 $$, $$ y = -2 $$
**Solutions:** - **Problem 14:** $$ x = 1 $$, $$ y = -2 $$ - **Problem 15:** $$ x = -3 $$, $$ y = -2 $$

14. (7-2) Solve the system using substitution. 15. (7-4) Solve the system using elimination. \( \begin{array}{c}4 x+3 y=-2 \\ x+5 y=-9 \\ 3 x+3 y=-15 \\ 5 x-9 y=3\end{array} \)

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