Question

Resolva utilizando cortes:

a) $\left \{ {x + y = 11} \atop {x - y = 3 }} \right. b) \left \{ {{x - y = 1} \atop {x + y = 9}} \right. c) \left \{ {{x - y = 16} \atop {x + y = 74}} \right. d) \left \{ {{2x - y = 20} \atop {2x + y = 48}} \right. e) \left \{ {{2x - 3y = - 16} \atop {5x + 3y = 2}} \right. f) \left \{ {{3x + y = 0} \atop {11x - y = 42}} \right. g) \left \{ {{x + 3y = 5} \atop {2x - y = -4}} \right. h) \left \{ {{3x + 3y = 21} \atop {2x - y = 5}} \right. i) \left \{ {{x - y = 3} \atop {2x + 3y = 16}} \right.$

j ) $\left \{ {{5x + y = 5} \atop {10x - 2y = -2}} \right. k) \left \{ {{x - 3y = 0} \atop {2x - y = 1}} \right. l) \left \{ {{5x - y = 4} \atop {2x - y = -5}} \right.$

Answer 1

a)
x + y = 11
x - y =  3
2x = 14

x = 7

x + y = 11
7 + y = 11
y = 11 - 7

y = 4                S{(4;7)}

b)
x - y = 1
x + y = 9
2x = 10

x = 5

x + y = 9
5 + y = 9
y = 9 - 5

y = 4            S {(4;5)}

c)
x - y = 16
x + y = 74
2x = 90

x = 45

x + y = 74
45 + y = 74
y = 74 - 45

y = 29             S {(29;45)}

d)
2x - y = 20
2x + y = 48
4x = 68
x = 68/4

x = 17

2x + y = 48
2(17) + y = 48
34 + y = 48
y = 48 - 34

y = 14                S {(14;17)}
 
e)
2x  - 3y = -16
5x + 3y =    2
7x = -14
x = -14/2

x = -7

2x - 3y = -16
2(-7) - 3y = -16
-14 - 3y = 2
-3y = 2+14
-3y = 16

y = -16/3             S {(-16/3 ; -7)}

f)
 3x + y = 0
11x - y = 42
14x = 42
x = 42/14

x = 3

3(3) + y = 0
9 + y = 0

y = -9              S{(-9;3)}

g) 
  x + 3y =  5
2x  -   y = -4 (.3) multiplica por 3

  x + 3y =   5
6x  - 3y = -12 
----------------------
7x = -7
x = -7/7

x = -1

x + 3y = 5
-1 + 3y = 5
3y = 5 + 1
3y = 6
y = 6/3

y = 2                S {(-1;2)}

h)
3x + 3y = 21
2x -   y  =  5 (.3) multiplica por 3

3x + 3y = 21
6x -  3y = 15
-----------------
9x = 36
x = 36/4

x = 9

3x + 3y = 21
3(9) + 3y = 21
27 + 3y = 21
3y = 21 - 27
3y = -6
y = -6/3

y = -2                    S{(-2;9)}

i)
  x  -  y  =  3 (.3)
2x + 3y = 16

3x - 3y = 9
2x + 3y = 16
----------------
5x = 25
x = 25/5

x = 5

x  -  y  =  3
5 - y = 3
-y = 3 - 5
-y = -2 (-1)

y = 2                  S {(2;5)}

j)
  5x +  y =  5 (.2)
10x - 2y = -2

10x + 2y = 10
10x - 2y = -2
-----------------
20x = 8
x = 8/20

x = 2/5

x - y = 3
2/5 - y = 3
-y = 3 - 2/5
mmc=5
-y = 13/5 (-1)

y = -13/5            S {(-2/5 ; -13/5)}

k)
x - 3y = 0
2x - y = 1 (.-3)

   x - 3y = 0
-6x + 3y = -3
-----------------
-5x = -3

x = 3/5

x - 3y = 0
3/5 - 3y = 0
-3y = 3/5
y = 3/5 ÷ -3

y = -1/5                      S {(-1/5 ; 3/5)}

l)
5x - y = 4
2x - y = -5 (-1)

 5x - y = 4
-2x + y = +5
----------------
3x = 9

x = 3

5x - y = 4
5(3) - y = 4
15 - y = 4
-y = 4 - 15
-y = -11

y = 11                  S {(3;11)}