\begin{tabular}{l}\hline Question 9 N II Pause Q Zoom \ \hline \ Solve the system. \ $$ x+y=-1 $$ \ $$ 3 x-y=5 $$\end{tabular}

Question

UpStudy AI · Accepted Answer

To solve the given system of equations:

$$
\begin{cases}
x + y = -1 \quad \quad \quad \quad (1) \
3x - y = 5 \quad \quad \quad \quad (2)
\end{cases}
$$

we can use either the **elimination method** or the **substitution method**. Here, we'll demonstrate both methods.

---

### **1. Elimination Method**

**Step 1:** Add equations (1) and (2) to eliminate $$ y $$.

$$
\begin{align*}
(x + y) + (3x - y) &= -1 + 5 \
4x &= 4
\end{align*}
$$

**Step 2:** Solve for $$ x $$.

$$
x = \frac{4}{4} = 1
$$

**Step 3:** Substitute $$ x = 1 $$ back into equation (1) to find $$ y $$.

$$
1 + y = -1 \
y = -1 - 1 \
y = -2
$$

---

### **2. Substitution Method**

**Step 1:** Solve equation (1) for $$ y $$.

$$
y = -1 - x
$$

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

$$
3x - (-1 - x) = 5 \
3x + 1 + x = 5 \
4x + 1 = 5
$$

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

$$
4x = 5 - 1 \
4x = 4 \
x = \frac{4}{4} = 1
$$

**Step 4:** Substitute $$ x = 1 $$ back into $$ y = -1 - x $$ to find $$ y $$.

$$
y = -1 - 1 = -2
$$

---

### **Solution**

$$
\boxed{\,x = 1,\quad y = -2\,}
$$
The solution to the system is $$ x = 1 $$ and $$ y = -2 $$.

\begin{tabular}{l}\hline Question 9 N II Pause Q Zoom \\ \hline \\ Solve the system. \\ \( x+y=-1 \) \\ \( 3 x-y=5 \)\end{tabular}