Question

Resolva os sistemas pelo metodo da comparação. ​

Answer 1

a) {3x-4y=0

{5x+7y=41

$3x - 4y = 0 \\ 4y = 3x \\ y = \frac{3}{4}x$

$5x + 7y = 41 \\ 7y = 11 - 5x \\ y = \frac{11 - 5x}{7}$

$\frac{3}{4}x = \frac{11 - 5x}{7} \\ 21x = 44 - 20x \\ 21x + 20x = 44 \\ 41x = 44$

$x = \frac{44}{41}$

$y = \frac{3}{4}x \\ y = \frac{3}{4}. \frac{44}{41} \\ y = \frac{33}{41}$

b)

{2x+5y=21

{3x-y= -11

$2x + 5y = 21 \\ 5y = 21 - 2x \\ y = \frac{21 - 2x}{5}$

$3x - y = - 11 \\ y = 3x + 11$

$3x + 11 = \frac{21 - 2x}{5} \\15x + 55 = 21 - 2x \\ 15x + 2x = 21 - 55 \\ 17x = - 34$

$x = - \frac{34}{17} \\ x = - 2$

$y = 3x + 11 \\ y = 3.( - 2) + 11 \\ y = - 6 + 11 \\ y = 5$