Question

Determine x e y nos trapézios ao lado

Answer 1

a)
(3y + 18) + (x + y) = 180
4y + x + 18 = 180
4y + x = 162

(5y + 10) + (x - 22) = 180
5y + x - 12 = 180
5y + x = 192

$\left \{ {{4y+x=162\ \ \ \ \ \ \ } \atop {5y+x = 192\ \ .(-1)}} \right. \\ \\ \left \{ {{4y+x=162} \atop {-5y-x = -192}} \right. \\ \\ \\ Somando\ temos: \\ \\ -y=-30\\ y=30\\ \\ Substituindo:\\ 4y+x=162\\ 4.30+x=162\\ 120+x=162\\ x=42$

b)
3x+y = 4y+6
3x-3y=6 (:3)
x-y=2

(3x+y)+(5y+39) = 180
3x+6y=180-39
3x+6y=141
x+2y=47

$\left \{ {{x-y=2\\ .(-1)} \atop {x+2y=47}} \right. \\ \\ \left \{ {{-x+y=-2\\} \atop {x+2y=47}} \right. \\ \\ Somando:\\ \\ 3y=45\\ y=15\\ \\ Substituindo:\\ \\ x-y=2\\ x-15=2\\ x=17$

c)
2x+y=90

(4x - 18) + 3y = 180
4x + 3y = 198

$\left \{ {{2x+y=90\ .(-2)} \atop {4x+3y=198\ \ \ \ \ \ }} \right. \\ \\ \left \{ {{-4x-2y=-180} \atop {4x+3y=198}} \right. \\ \\ Somando:\\ \\ y = 18\\ \\ Substituindo:\\ \\ 2x+y=90 \\ 2x+18=90 \\ 2x=72 \\ x=36$

=)