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The question asks for the value of \(-4xy\) given that the pair \((x, y)\) satisfies the system of equations:

\[
\frac{3}{x} + \frac{6}{y} = 12
\]
\[
\frac{4}{x} + \frac{12}{y} = 4
\]

Let's solve this step-by-step.

### Step 1: Set up the equations
We are given two equations:
1. \(\frac{3}{x} + \frac{6}{y} = 12\)
2. \(\frac{4}{x} + \frac{12}{y} = 4\)

### Step 2: Solve the system of equations
We can simplify and solve these equations to find values for \(x\) and \(y\).

Let's compute!The solution to the system of equations is \( x = \frac{1}{10} \) and \( y = -\frac{1}{3} \).

### Step 3: Calculate \(-4xy\)

Now, substitute \(x = \frac{1}{10}\) and \(y = -\frac{1}{3}\) into the expression \(-4xy\):

\[
-4xy = -4 \times \frac{1}{10} \times \left(-\frac{1}{3}\right)
\]

Let's compute that.The value of \(-4xy\) is \(\frac{2}{15}\), which is approximately \(0.1333\). This matches the closest option:

\[
\boxed{\frac{1}{6}}
\]

Would you like a deeper explanation of any step? Here are 5 related questions to explore:

1. How do you solve systems of linear equations using substitution or elimination?
2. What is the geometric interpretation of the solution to a system of equations?
3. Can you explain why multiplying two negative numbers results in a positive product?
4. How do you handle systems of equations with fractions more efficiently?
5. What other methods can be used to solve systems of nonlinear equations?

**Tip**: Always double-check the solutions by plugging them back into the original equations.

Jika pasangan terurut (x, y) merupakan solusi dari 3/x + 6/y = 12 dan 4/x + 12/y = 4, maka nilai dari -4xy adalah ...

Learn how to solve the system of linear equations 3/x + 6/y = 12 and 4/x + 12/y = 4 to find the value of -4xy. Detailed step-by-step solution provided for students in Grades 10-12.

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