Question

x = 4y
x + 2y = 12
(some hand - written calculation steps and a coordinate grid with a line and some points)

Explanation:

Step1: Identify the system of equations

We have the system:
\[

$$\begin{cases} x = 4y \\ x + 2y = 12 \end{cases}$$

\]

Step2: Substitute \(x = 4y\) into the second equation

Substitute \(x\) in \(x + 2y = 12\) with \(4y\):
\[
4y + 2y = 12
\]

Step3: Combine like terms

Combine \(4y\) and \(2y\):
\[
6y = 12
\]

Step4: Solve for \(y\)

Divide both sides by 6:
\[
y = \frac{12}{6} = 2
\]

Step5: Solve for \(x\)

Substitute \(y = 2\) into \(x = 4y\):
\[
x = 4\times2 = 8
\]

Answer:

The solution to the system of equations is \(x = 8\) and \(y = 2\).