Question

evaluate the following expression for (a) \\(x = 4\\) and \\(y = 1\\) and (b) \\(x = 1\\) and \\(y = 3\\).

\\\frac{4x + 8y}{5x + 8y}\\

(a) for \\(x = 4\\) and \\(y = 1\\), \\\\ \frac{4x + 8y}{5x + 8y} = \square
(type an integer or a simplified fraction.)

Explanation:

Substitute the given values into the expression

$$ \text{For } x = 4 \text{ and } y = 1: $$

$$ \frac{4(4) + 8(1)}{5(4) + 8(1)} $$

Simplify the numerator and denominator

$$ \text{Numerator: } 4(4) + 8(1) = 16 + 8 = 24 $$

$$ \text{Denominator: } 5(4) + 8(1) = 20 + 8 = 28 $$

$$ \text{Fraction: } \frac{24}{28} $$

Reduce the fraction to simplest form

$$ \frac{24 \div 4}{28 \div 4} = \frac{6}{7} $$

Answer:

(a) For \(x = 4\) and \(y = 1\), \(\frac{4x + 8y}{5x + 8y} =\) <blank>\(\frac{6}{7}\)</blank>