a)
[tex] \frac{5x + 2y}{2x + y} = \frac{69}{29} \\ 29 \times (5x + 2y) = 69 \times (2x + y) \\ 145x + 58y = 138x + 69y \\ 145x - 138x = 69y - 58y \\ 7x = 11y = > \frac{x}{y} = \frac{11}{7} = > \frac{y}{x} = \frac{7}{11} [/tex]
b)
[tex] \frac{2x + y}{x + 2y} = \frac{13}{17} \\ 17 \times (2x + y) = 13 \times (x + 2y) \\ 34x + 17y = 13x + 26y \\ 34x - 13x = 26y - 17y \\ 21x = 9y = > 7x = 3y = > \\ \frac{x}{y} = \frac{3}{7} = > \frac{y}{x} = \frac{7}{3} [/tex]
c)
[tex] \frac{3x - y}{2y} = \frac{9}{4} \\ 4 \times (3x - y) = 9 \times 2y \\ 12x - 4y = 18y \\ 12x = 22y < = > 6x = 11y \\ \frac{x}{y} = \frac{11}{6} = > \frac{y}{x} = \frac{6}{11} [/tex]
