Respostas
Explicação passo-a-passo:
x + y = 10
x – y = 4
x = 10 – y → x – y = 4 x + y = 10
10 – y – y = 4 x + 3 = 10
–2y = 4 – 10 x = 7 → S = {(7, 3)}
2y = 6
y = 3
2
x + y = –11
x – y = 1
x = 1 + y → x + y = –11 x – y = 1
1 + y + y = –11 x – (–6) = 1
2y = –12 x + 6 = 1
y = –6 x = –5
x2
– 2xy + y2
=
= (–5)2
– 2 · (–5) · (–6) + (–6)2
=
= 25 + 10 · (–6) + 36 =
= 61 – 60 = 1
Agora é com você! (página 52)
1 +
+ =
− = −
x y
x y
2 7
3 2 3
4x = 4
x = 1 → x + 2y = 7
1 + 2y = 7
2y = 7 – 1 → 2y = 6 → y = 3
S = {(1, 3)}
2 A
2 3 4
3 2 1
4 6 8
9 6 3
2
3
x y
x y
x y
x y
+ =
+ =
→ + − − = −
+ =
⋅ −
⋅
( )
( )
5x = –5
x = –1 → 2x + 3y = 4
–2 + 3y = 4
3y = 6
y = 2
x y
x y
2 2 1 2
1 2
1 2
1
1 −
+ = − −
− + = − = − ( )
Testando seus conhecimentos (página 53)
1 a)
x + y = 14
x + 3y = 20
x = 14 – y
x = 14 – 3
14 – y + 3y = 20 x = 11
2y = 6
y = 3
S = {(11, 3)}
b)
x – 2y = 3
x + 4y = 9
x = 3 + 2y
x = 3 + 2
3 + 2y + 4y = 9 x = 5
6y = 6
y = 1
S = {(5, 1)}
c)
x + y = 2
y = 3x
x + 3x = 2
4x = 2
x
x
y
y
S
=
=
= ⋅
=
=
2
4
1
2
3 1
2
3
2
1
2
3
2 ,
x
x
y
y
S
=
=
= ⋅
=
=
2
4
1
2
3 1
2
3
2
1
2
3
2 ,
d)
2x + y = 10
x + 2y = 11
y = 10 – 2x
y = 10 – 6
x + 2 · (10 – 2x) = 11 y = 4
x + 20 – 4x = 11
–3x = –9
x = 3
S = {(3, 4)}
2 a)
x – y = 7
x + y = 23 15 + y = 23
y = 23 – 15
y = 8
2x = 30
x = 15
S = {(15, 8)}
+
b)
3x + y = 23
x – 3y = 1 · (–3)
3x + y = 23
–3x + 9y = –3
3x + 2 = 23
3x = 21
10y = 20 x = 7
y = 2
S = {(7, 2)}