B: For each pair of simultaneous equations: \begin{tabular}{|l|}\hline\( x+y=13 \) and \( 8 x-5 y=0 \) \\ \( x+y=21 \) and \( 13 x-8 y=0 \)\end{tabular} 1. Solve for \( x \) and \( y \). 2. Find the value of the ratio \( \frac{x}{y} \). Write the ratio \( \frac{x}{y} \) in decimal form correct to three decimal places where possible. 3.

To solve the simultaneous equations, let's start with the first pair: 1. For the equations \( x+y=13 \) and \( 8x-5y=0 \): From \( x+y=13 \), we can express \( y = 13 - x \). Substitute \( y \) into the second equation: \( 8x - 5(13 - x) = 0 \) This simplifies to \( 8x - 65 + 5x = 0 \) or \( 13x = 65 \). Thus, \( x = 5 \). Now substitute back to find \( y \): \( y = 13 - 5 = 8 \). So, \( (x, y) = (5, 8) \). 2. The ratio \( \frac{x}{y} \): Using the values obtained, we find \( \frac{x}{y} = \frac{5}{8} = 0.625 \) (correct to three decimal places). Now let's move on to the second pair of equations: 1. For \( x+y=21 \) and \( 13x-8y=0 \): From \( x+y=21 \), express \( y = 21 - x \). Substitute \( y \) into the second equation: \( 13x - 8(21-x) = 0 \) This simplifies to \( 13x - 168 + 8x = 0 \) or \( 21x = 168 \). Thus, \( x = 8 \). Now substitute back to find \( y \): \( y = 21 - 8 = 13 \). So, \( (x, y) = (8, 13) \). 2. The ratio \( \frac{x}{y} \): Now with these values, \( \frac{x}{y} = \frac{8}{13} \approx 0.615 \) (correct to three decimal places). In summary: For the first pair, \( (x, y) = (5, 8) \) yields a ratio of \( 0.625 \). For the second pair, \( (x, y) = (8, 13) \) gives a ratio of \( 0.615 \).