olve the system by substitution. $$ \qquad \begin{array}{l}y=x-15 \ y=4 x\end{array} $$

Question

UpStudy AI · Accepted Answer

Certainly! Let's solve the given system of equations by substitution:

$$
\begin{cases}
y = x - 15 \
y = 4x
\end{cases}
$$

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

Since both equations equal $$ y $$, we can set them equal:

$$
x - 15 = 4x
$$

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

Subtract $$ x $$ from both sides to get:

$$
-15 = 3x
$$

Now, divide both sides by 3:

$$
x = \frac{-15}{3} = -5
$$

**Step 3: Substitute $$ x $$ back into one of the original equations to find $$ y $$.**

Using $$ y = 4x $$:

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

**Solution:**

$$
x = -5 \quad \text{and} \quad y = -20
$$

So, the solution to the system is:

$$
(x, y) = (-5, -20)
$$
The solution is $$ x = -5 $$ and $$ y = -20 $$.

olve the system by substitution.