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} = \frac{6}{7}\\\\\\)
(type an integer or a simplified fraction.)

(b) for \\(x = 1\\) and \\(y = 3\\), \\\\(\frac{4x + 8y}{5x + 8y} = \square\\\\\\)
(type an integer or a simplified fraction.)

Explanation:

Substitute the values into the expression

$$ \text{For } x = 1 \text{ and } y = 3: $$

$$ \frac{4(1) + 8(3)}{5(1) + 8(3)} $$

Simplify the numerator and denominator

$$ \frac{4 + 24}{5 + 24} = \frac{28}{29} $$

Verify the fraction is in simplest form

$$ \text{Since 29 is a prime number, } \frac{28}{29} \text{ cannot be simplified further.} $$

Answer:

For \(x = 1\) and \(y = 3\), \(\frac{4x+8y}{5x+8y} =\) <blank>\(\frac{28}{29}\)</blank>