Question

ESSA É A ULTIMA!
$I) \left \{ {{ \frac{X+Y}{8}= \frac{X+Y}{3} } \atop { \frac{5X}{3}=-2Y-1 }} \right. J) \left \{ {{ \frac{x}{5} + \frac{y}{3}= \frac{2}{15} } \atop {2(x-3)+3(y-2)=-12}} \right. K) \left \{ {{ \frac{X+Y}{3}+ \frac{X-Y}{2} = \frac{1}{6} } \atop {2(X-1)-2Y=X-2}} \right. L) \left \{ {{ \frac{X+Y}{12}+ \frac{X-Y}{8}= \frac{11}{12} } \atop { \frac{X-Y}{9}+ \frac{X+Y}{6}= \frac{14}{9} }} \right.$

Answer 1

Boa noite Adrian

I)

(x + y)/8 = (x + y)/3,
5x/3 = -2y - 1

3x + 3y = 8x + 8y
5x + 5y = 0
x + y = 0
y = -x

5x = -6y - 3
5x + 6y = -3
5x - 6x = -3
-x = -3
x = 3
y = -x = -3

S = (3, -3)


J) 

x/5 + y/3 = 2/15,
2*(x - 3) + 3*(y - 2) = -12

3x + 5y = 2
2x - 6 + 3y - 6 = -12

3x + 5y = 2
2x + 3y = 0

9x + 15y = 6 
10x + 15y = 0
10x - 9x = -6
x = -6

-12 + 3y = 0
3y = 12
y = 4 

S = (-6, 4)

K) 

(x + y)/3 + (x - y)/2 = 1/6 ,
2*(x - 1) - 2y =  x - 2

2x + 2y + 3x - 3y = 1
5x - y = 1
2x - 2 - 2y - x + 2 = 0
x - 2y = 0

10x - 2y = 2
-x + 2y = 0
9x = 2
x = 2/9
2y = 2/9
y = 1/9 

L)

(x + y)/12 + (x - y)/8 = 11/12,
(x - y)/9  + (x + y)/6 = 14/9

2x + 2y + 3x - 3y = 22
5x - y = 22

2*(x - y)/18 + 3*(x + y)/18 = 28/18
2x - 2y + 3x + 3y = 28

5x + y = 28
5x - y = 22
10x = 50
x = 5
25 + y = 28
y = 3 

S = (5, 3)