Question

\

$$\begin{cases}2x + 8y = 1\\\\x = 2y\\end{cases}$$

Explanation:

Step1: Substitute \( x = 2y \) into the first equation

We have the system of equations \(

$$\begin{cases}2x + 8y = 1\\x = 2y\end{cases}$$

\). Substitute \( x = 2y \) into \( 2x + 8y = 1 \), we get \( 2(2y)+8y = 1 \).

Step2: Simplify and solve for \( y \)

Simplify the left - hand side of the equation \( 2(2y)+8y = 1 \): \( 4y+8y = 1 \), which combines to \( 12y = 1 \). Then, solve for \( y \) by dividing both sides by 12: \( y=\frac{1}{12} \).

Step3: Substitute \( y=\frac{1}{12} \) back to find \( x \)

Substitute \( y = \frac{1}{12} \) into the equation \( x = 2y \). So, \( x=2\times\frac{1}{12}=\frac{1}{6} \).

Answer:

The solution of the system of equations is \( x = \frac{1}{6} \), \( y=\frac{1}{12} \)