Solve the system by substitution. $$ \begin{aligned}-3 x-6 y & =45 \ -5 y & =x\end{aligned} $$

Question

UpStudy AI · Accepted Answer

To solve the system of equations by substitution:

$$
\begin{aligned}
-3x - 6y &= 45 \quad \text{(1)} \
-5y &= x \quad \text{(2)}
\end{aligned}
$$

**Step 1: Solve Equation (2) for $$ x $$.**

From equation (2):
$$
x = -5y
$$

**Step 2: Substitute $$ x = -5y $$ into Equation (1).**

$$
-3(-5y) - 6y = 45
$$

Simplify:
$$
15y - 6y = 45
$$
$$
9y = 45
$$

**Step 3: Solve for $$ y $$.**

$$
y = \frac{45}{9} = 5
$$

**Step 4: Substitute $$ y = 5 $$ back into $$ x = -5y $$ to find $$ x $$.**

$$
x = -5(5) = -25
$$

**Solution:**
$$
x = -25 \quad \text{and} \quad y = 5
$$
$$ x = -25 $$ and $$ y = 5 $$.

Solve the system by substitution.