Evaluate the algebraic expression at the indicated values of the variables.6x−y/x^2−6y at x=−5 and y=−3

Given an exact, simplified answer.  

Given an approximate answer, rounded to 3 decimal places.  

To evaluate the algebraic expression \(\frac{6x - y}{x^2 - 6y}\) at \(x = -5\) and \(y = -3\), we substitute the values of \(x\) and \(y\) into the expression.

The expression is:

\[
\frac{6x - y}{x^2 - 6y}
\]

### Step-by-Step Solution:

1. **Substitute** \(x = -5\) and \(y = -3\) into the expression:

\[
6(-5) - (-3) = -30 + 3 = -27
\]

\[
x^2 - 6y = (-5)^2 - 6(-3) = 25 + 18 = 43
\]

2. **Plug these values** into the expression:

\[
\frac{-27}{43}
\]

### Exact Simplified Answer:

\[
\frac{-27}{43}
\]

### Approximate Answer (Rounded to 3 Decimal Places):

\[
-0.628
\]

Would you like more details or have any questions?

Here are 5 questions related to this problem:

1. How do you determine the numerator and denominator when substituting values?
2. Why is it important to simplify the exact expression before approximating?
3. What is the significance of rounding to 3 decimal places in mathematics?
4. How do you handle negative signs when evaluating algebraic expressions?
5. What are some common mistakes to avoid when substituting values into expressions?

**Tip:** When substituting values into an expression, always double-check signs and arithmetic operations to avoid mistakes.

Evaluate the algebraic expression at the indicated values of the variables: 6x − y / x^2 − 6y at x = −5 and y = −3. Give an exact, simplified answer and an approximate answer rounded to 3 decimal places.

Evaluate the algebraic expression (6x - y) / (x^2 - 6y) at x = -5 and y = -3. This problem involves substitution and simplification of algebraic expressions. Detailed step-by-step solution provided with exact and approximate answers. Suitable for students in Grades 8-10.

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