resolva os sistemas de equações com duas incógnitas a seguir. pelo método de adição
a) 7a-b=-5
a+b=-1
b)b=15a+17
5a+2b=13
c) 4m+n=7
m+n\2=3
d)7x+8y=52
x=10+4y
e) 2x+3y=57
2y-x=38
f) p=5q+1
p=52-2q/3
g) 4x+6y=27
x+y=5
h) 2x-y=3
3x+y=3
i)-w+v=5
2w-v=2
j) 2m+3n=4
m+n=2
k) x+y=3
x-y=9
l) 2x-2y=12
x-2y=0
m) x+y=7
x+2y=11
n) x+y=17
x-y=1
Respostas
a)
7a - b= - 5
a + b= - 1 (+)
-----------------
8a = - 6 (:2)
4a = - 3
a = - 3/4
a + b = - 1
-3/4 + b = - 1
b = - 1 + 3/4
b = (- 4.1 + 3)/4
b = (-4 + 3)/4
b = - 1/4
b)
b=15a+17
5a+2b=13
- 15a + b = 17 .(-2)
5a + 2b = 13
30a - 2b = - 34
5a + 2b = 13 (+)
-------------------------
35a = - 21 (:7)
5a = - 3
a = - 3/5
b = 15a + 17
b = 15.(-3)/5 + 17
b = - 45/5 + 17
b = - 9 + 17
b = 8
c)
4m + n = 7
m+n/2 = 3
4m + n = 7
(2m + n)/2 = 3.2/2
4m + n = 7
2m + n = 6 (-1)
4m + n = 7
- 2m - n = - 6 (+)
-----------------------
2m = 1
m = 1/2
2m + n = 6
2.1/2 + n = 6
2/2 + n = 6
1 + n = 6
n = 6 - 1
n = 5
d)
7x+8y=52
x=10+4y
7x + 8y = 52
x - 4y = 10 (2)
7x + 8y = 52
2x - 8y = 20 (+)
------------------------
9x = 72
x = 72/9
x = 8
x - 4y = 10
8 - 4y = 10
8 - 10 = 4y
- 2 = 4y
4y = - 2 (:2)
2y = - 1
y = - 1/2
e)
2x + 3y=57
2y-x=38
2x + 3y = 57
- x + 2y = 38 (2)
2x + 3y = 57
- 2x + 4y = 76 (+)
--------------------------
7y = 133
y = 133/7
y = 19
- x + 2y = 38
- x + 2.19 = 38
- x + 38 = 38
38 - 38 = x
0 = x
x = 0
f)
p=5q+1
p=52-2q/3
p - 5q = 1
p + 2q/3 = 52
p - 5q = 1
(3p + 2q)/3 = 3.52/3
p - 5q = 1 (-3)
3p + 2q = 156
- 3p + 15q = - 3
3p + 2q = 156 (+)
------------------------
17q = 153
q = 153/17
q = 9
p - 5q = 1
p - 5.9 = 1
p - 45 = 1
p = 1 + 45
p = 46
g)
4x+6y=27
x+y=5 (-4)
4x + 6y = 27
- 4x - 4y = - 20 (+)
-----------------------------
2y = 7
y = 7/2
x + y = 5
x + 7/2 = 5
x = 5 - 7/2
x = (2.5 - 7)/2
x = (10 - 7)/2
x = 3/2
h)
2x-y=3
3x+y=3 (+)
-----------------
5x = 6
x = 6/5
2x - y = 3
2.6/5 - y = 3
12/5 - y = 3
12/5 - 3 = y
(12 - 5.3)/5 = y
(12 - 15)/5 = y
- 3/5 = y
y = - 3/5
i)
-w+v=5
2w-v=2 (+)
-----------------
w = 7
- w + v = 5
- 7 + v = 5
v = 5 + 7
v = 12
j)
2m + 3n = 4
m + n=2 (-2)
2m + 3n = 4
- 2m - 2n = - 4 (+)
---------------------------
n = 0
M + n = 2
M + 0 = 2
m = 2
k)
x+y=3
x-y=9 (+)
-----------
2x = 12
x = 12/2
x = 6
x + y = 3
6 + y = 3
y = 3 - 6
Y = - 3
l)
2x-2y=12
x-2y=0 (-1)
2x - 2y = 12
- x + 2y = 0 (+)
-------------------
x = 12
x - 2y = 0
12 = 2y
2y = 12
y = 12/2
y = 6
m)
x+y=7 (-1)
x+2y=11
- x - y = - 7
x + 2y = 11 (+)
---------------------
y = 4
x + y = 7
x + 4 = 7
x = 7 - 4
x = 3
n)
x+y=17
x-y=1 (+)
--------------
2x = 18
x = 18/2
x = 9
x + y = 17
9 + y = 17
y = 17 - 9
y = 8