Solve the system of equations. $$ \begin{array}{l}y=x+16 \ y=5 x-12 \ x=\square\end{array} $$ $$ y $$

Question

UpStudy AI · Accepted Answer

To solve the system of equations:

$$
\begin{cases}
y = x + 16 \
y = 5x - 12
\end{cases}
$$

**Step 1: Set the equations equal to each other**

Since both expressions equal $$ y $$, set them equal to each other:

$$
x + 16 = 5x - 12
$$

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

Subtract $$ x $$ from both sides:

$$
16 = 4x - 12
$$

Add 12 to both sides:

$$
28 = 4x
$$

Divide by 4:

$$
x = 7
$$

**Step 3: Solve for $$ y $$**

Substitute $$ x = 7 $$ into one of the original equations, for example, $$ y = x + 16 $$:

$$
y = 7 + 16 = 23
$$

**Solution:**

$$
x = 7 \quad \text{and} \quad y = 23
$$
$$ x = 7 $$ and $$ y = 23 $$.

Solve the system of equations. \[ \begin{array}{l}y=x+16 \\ y=5 x-12 \\ x=\square\end{array} \] \( y \)