4) $$ \begin{array}{c}y=-6 x-1 \ x+y=19\end{array} $$

Question

UpStudy AI · Accepted Answer

To solve the system of equations:

$$
\begin{cases}
y = -6x - 1 \
x + y = 19
\end{cases}
$$

**Step 1:** Substitute the expression for $$ y $$ from the first equation into the second equation.

$$
x + (-6x - 1) = 19
$$

**Step 2:** Simplify the equation.

$$
x - 6x - 1 = 19 \
-5x - 1 = 19
$$

**Step 3:** Add 1 to both sides to isolate the term with $$ x $$.

$$
-5x = 20
$$

**Step 4:** Divide both sides by -5 to solve for $$ x $$.

$$
x = \frac{20}{-5} \
x = -4
$$

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

$$
y = -6(-4) - 1 \
y = 24 - 1 \
y = 23
$$

**Solution:**
$$
x = -4 \quad \text{and} \quad y = 23
$$
$$ x = -4 $$ and $$ y = 23 $$.

4) \( \begin{array}{c}y=-6 x-1 \\ x+y=19\end{array} \)