$$ 8 \left\{ \begin{array} { l } { 3 x - 7 y = 41 } \ { x = - 2 y - 21 } \end{array} ight. $$

Question

$$ 8 \left\{ \begin{array} { l } { 3 x - 7 y = 41 } \ { x = - 2 y - 21 } \end{array} ight. $$

UpStudy AI · Accepted Answer

Certainly! Let's solve the given system of equations step by step.

$$
\begin{cases}
3x - 7y = 41 \
x = -2y - 21
\end{cases}
$$

**Step 1: Substitute the Expression for $$ x $$ into the First Equation**

We are given $$ x $$ in terms of $$ y $$ from the second equation:

$$
x = -2y - 21
$$

Substitute this expression for $$ x $$ into the first equation:

$$
3(-2y - 21) - 7y = 41
$$

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

Expand the equation:

$$
-6y - 63 - 7y = 41
$$

Combine like terms:

$$
-13y - 63 = 41
$$

Add 63 to both sides:

$$
-13y = 104
$$

Divide both sides by -13:

$$
y = \frac{104}{-13} \
y = -8
$$

**Step 3: Substitute $$ y = -8 $$ Back into the Expression for $$ x $$**

Using the second equation:

$$
x = -2y - 21 \
x = -2(-8) - 21 \
x = 16 - 21 \
x = -5
$$

**Solution:**

$$
x = -5 \
y = -8
$$
$$ x = -5 $$ and $$ y = -8 $$.

\( 8 \left\{ \begin{array} { l } { 3 x - 7 y = 41 } \\ { x = - 2 y - 21 } \end{array} \right. \)