15. $$ \begin{array}{l}x+2 y=5 \ 3 x+y=-8\end{array} $$

Question

UpStudy AI · Accepted Answer

To solve the system of equations:

$$
\begin{cases}
x + 2y = 5 \quad \text{(1)} \
3x + y = -8 \quad \text{(2)}
\end{cases}
$$

we can use the **substitution method**. Here's a step-by-step solution:

### Step 1: Solve Equation (1) for $$ x $$

From equation (1):

$$
x + 2y = 5 \
\Rightarrow x = 5 - 2y
$$

### Step 2: Substitute $$ x $$ into Equation (2)

Substitute $$ x = 5 - 2y $$ into equation (2):

$$
3x + y = -8 \
3(5 - 2y) + y = -8 \
15 - 6y + y = -8 \
15 - 5y = -8
$$

### Step 3: Solve for $$ y $$

$$
15 - 5y = -8 \
-5y = -8 - 15 \
-5y = -23 \
y = \frac{-23}{-5} \
y = \frac{23}{5} \quad \text{or} \quad 4.6
$$

### Step 4: Substitute $$ y $$ Back into the Expression for $$ x $$

Using $$ x = 5 - 2y $$:

$$
x = 5 - 2\left(\frac{23}{5}\right) \
x = 5 - \frac{46}{5} \
x = \frac{25}{5} - \frac{46}{5} \
x = \frac{-21}{5} \quad \text{or} \quad -4.2
$$

### **Solution**

$$
x = -\frac{21}{5} \quad \text{and} \quad y = \frac{23}{5}
$$

Or in decimal form:

$$
x = -4.2 \quad \text{and} \quad y = 4.6
$$
The solution to the system of equations is $$ x = -\frac{21}{5} $$ and $$ y = \frac{23}{5} $$.

15. \( \begin{array}{l}x+2 y=5 \\ 3 x+y=-8\end{array} \)