4) $$ \begin{array}{r}-3 x-3 y=3 \ y=-5 x-17\end{array} $$

Question

UpStudy AI · Accepted Answer

To solve the system of equations:

$$
\begin{cases}
-3x - 3y = 3 \
y = -5x - 17
\end{cases}
$$

we can use the **substitution method**, since the second equation already expresses $$ y $$ in terms of $$ x $$.

### Step 1: Substitute $$ y $$ from the Second Equation into the First Equation

Given:
$$
y = -5x - 17
$$

Substitute this into the first equation:
$$
-3x - 3(-5x - 17) = 3
$$

### Step 2: Simplify the Equation

$$
-3x + 15x + 51 = 3
$$

Combine like terms:
$$
12x + 51 = 3
$$

### Step 3: Solve for $$ x $$

Subtract 51 from both sides:
$$
12x = 3 - 51
$$
$$
12x = -48
$$

Divide both sides by 12:
$$
x = \frac{-48}{12} = -4
$$

### Step 4: Substitute $$ x = -4 $$ Back into the Second Equation to Find $$ y $$

$$
y = -5(-4) - 17
$$
$$
y = 20 - 17
$$
$$
y = 3
$$

### **Solution**

$$
x = -4 \
y = 3
$$

**Therefore, the solution to the system of equations is $$ x = -4 $$ and $$ y = 3 $$.**
The solution is $$ x = -4 $$ and $$ y = 3 $$.

4) \( \begin{array}{r}-3 x-3 y=3 \\ y=-5 x-17\end{array} \)