4. $$ \begin{array}{l}y=-3 x-9 \ 5 x+2 y=-16\end{array} $$

Question

UpStudy AI · Accepted Answer

Sure, let's solve the system of equations step by step:

$$
\begin{cases}
y = -3x - 9 \quad \text{(1)} \
5x + 2y = -16 \quad \text{(2)}
\end{cases}
$$

**Step 1: Substitute Equation (1) into Equation (2)**

Since Equation (1) gives $$ y $$ in terms of $$ x $$, we can substitute $$ y = -3x - 9 $$ into Equation (2):

$$
5x + 2(-3x - 9) = -16
$$

**Step 2: Simplify and Solve for $$ x $$**

$$
5x - 6x - 18 = -16 \
- x - 18 = -16
$$

Add 18 to both sides:

$$
- x = 2
$$

Multiply both sides by -1:

$$
x = -2
$$

**Step 3: Substitute $$ x = -2 $$ Back into Equation (1) to Find $$ y $$**

$$
y = -3(-2) - 9 \
y = 6 - 9 \
y = -3
$$

**Solution:**

$$
x = -2 \
y = -3
$$
The solution is $$ x = -2 $$ and $$ y = -3 $$.

4. \( \begin{array}{l}y=-3 x-9 \\ 5 x+2 y=-16\end{array} \)