Question

(FME 1) Resolver os sistemas de equações:

a) $\left \{ {1/(x-y) + 1/ (x+y) = 3/4} \atop {1/ (x-y) - 1/ (x+y) = -1/4} } \right.$

Sugestão: faça 1/ (x-y) = a e 1/ (x+y) = b

b) $\left \{ {{3/( x + y +1) - 2/( 2x - y + 3) = 5/12 } \atop {2/( x + y +1) + 3/( 2x - y + 3) = 1}} \right.$

Answer 1

$A)\\\\\frac{1}{x-y} = a\\\frac{1}{x+y}=b\\\left \{a + b = \frac{3}{4} \\} \atop a - b= -\frac{1}{4} \\}} \right. \\\\Somando:\\\\2a = \frac{2}{4} \\a = \frac{1}{4}\\\frac{1}{x-y} = \frac{1}{4}\\x - y = 4\\x = 4 + y\\\\\frac{1}{4} + b = 3/4\\ \frac{1}{x+y} = \frac{2}{4} \\ \frac{1}{x+y} = \frac{1}{2}\\x + y = 2\\y + 4 + y = 2\\y = -1\\\\x = 4 + y\\x = 4 -1\\x = 3\\\\\\\left \{ {{x=3} \atop {y=-1}} \right.$

B) é análoga