b. $$ \begin{array}{l}3 y-15 x=-18 \ -3 y+6 x=-54\end{array} $$

Question

UpStudy AI · Accepted Answer

To solve the system of equations:

$$
\begin{cases}
3y - 15x = -18 \
-3y + 6x = -54 \
\end{cases}
$$

we can use the **elimination method** to find the values of $$ x $$ and $$ y $$.

### Step 1: Add the Two Equations to Eliminate $$ y $$

$$
\begin{align*}
(3y - 15x) + (-3y + 6x) &= -18 + (-54) \
3y - 15x - 3y + 6x &= -72 \
(-15x + 6x) &= -72 \
-9x &= -72
\end{align*}
$$

### Step 2: Solve for $$ x $$

$$
-9x = -72 \
x = \frac{-72}{-9} \
x = 8
$$

### Step 3: Substitute $$ x = 8 $$ into One of the Original Equations to Find $$ y $$

Let's use the first equation:

$$
3y - 15x = -18 \
3y - 15(8) = -18 \
3y - 120 = -18 \
3y = -18 + 120 \
3y = 102 \
y = \frac{102}{3} \
y = 34
$$

### Step 4: Verify the Solution

Plugging $$ x = 8 $$ and $$ y = 34 $$ into the second equation to ensure correctness:

$$
-3y + 6x = -54 \
-3(34) + 6(8) = -54 \
-102 + 48 = -54 \
-54 = -54 \quad \text{✓}
$$

### **Solution**

$$
\boxed{
\begin{cases}
x = 8 \
y = 34 \
\end{cases}
}
$$
$$ x = 8 $$ and $$ y = 34 $$.

b. \( \begin{array}{l}3 y-15 x=-18 \\ -3 y+6 x=-54\end{array} \)