15. What is the value of $$ y $$ in the following system of equations? $$ \begin{array}{l}y=4 x-12 \ y=10 x-42\end{array} $$

Question

UpStudy AI · Accepted Answer

To find the value of $$ y $$ in the given system of equations:

$$
\begin{cases}
y = 4x - 12 \
y = 10x - 42
\end{cases}
$$

We can solve this system using the **substitution method** since both equations are already solved for $$ y $$.

1. **Set the two expressions for $$ y $$ equal to each other:**

$$
4x - 12 = 10x - 42
$$

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

First, subtract $$ 4x $$ from both sides to get the $$ x $$-terms on one side:

$$
-12 = 6x - 42
$$

Next, add $$ 42 $$ to both sides to isolate the term with $$ x $$:

$$
30 = 6x
$$

Now, divide both sides by $$ 6 $$:

$$
x = 5
$$

3. **Substitute $$ x = 5 $$ back into one of the original equations to find $$ y $$.** We'll use the first equation:

$$
y = 4x - 12
$$

Plugging in $$ x = 5 $$:

$$
y = 4(5) - 12 = 20 - 12 = 8
$$

**So, the value of $$ y $$ is 8.**
$$ y = 8 $$

15. What is the value of \( y \) in the following system of equations? \[ \begin{array}{l}y=4 x-12 \\ y=10 x-42\end{array} \]