https://file.aiquickdraw.com/mathbot/file/17292066813757r60lisi.jpg

Let's solve the system of equations given in the image:

The system is:

\[
x + 4y = 30 \quad \text{(Equation 1)}
\]
\[
x = 2y \quad \text{(Equation 2)}
\]

### Step 1: Substitute Equation 2 into Equation 1
Since \( x = 2y \), substitute this into Equation 1:

\[
2y + 4y = 30
\]

### Step 2: Solve for \( y \)
Combine the terms:

\[
6y = 30
\]

Now, solve for \( y \):

\[
y = \frac{30}{6} = 5
\]

### Step 3: Solve for \( x \)
Now that we have \( y = 5 \), substitute it back into Equation 2 to find \( x \):

\[
x = 2y = 2(5) = 10
\]

### Solution:
The solution to the system is \( (x, y) = (10, 5) \).

### Correct Option:
The correct answer is the last option: \( (10, 5) \).

Would you like more details or have any questions?

Here are 5 relative questions to explore further:
1. What method can be used to solve a system of linear equations other than substitution?
2. How do we interpret the graphical representation of these two equations?
3. What happens if the two equations represent parallel lines?
4. Can this method be extended to systems with three variables?
5. How would the solution change if one of the coefficients was different?

**Tip:** When solving systems of equations, always simplify one equation as much as possible before substitution to reduce complexity.

Find the solution to the system of equations: x + 4y = 30 and x = 2y. Which option is correct?

Learn how to solve the linear system of equations x + 4y = 30 and x = 2y using the substitution method. This problem is ideal for students in Grades 8-10, covering key algebraic concepts like solving for variables and understanding linear equations.

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