SISTEMA DE ECUACIONES - 10

a)
x y 3
2x  y  0
1+𝑦 =3
3𝑥 = 3
𝑥=1
𝑦 = 3−1
𝑦=2
y
 1
b)
2
3x  2 y  1
5x 
𝑥=−
5
= −0.29
17
𝑦=−
16
= −0.94
17
c)
10 x  5 y  0
21x  7 y  28
−10𝑥 − 5 (
(−10𝑥 − 5𝑦 = 0) × 21
−10𝑥 +
280
35
−56
)
35
=0
=0
(21𝑥 − 7𝑦 = 28) × 10
−350𝑥 + 280 = 0
28
𝑥 = 35
−210𝑥 − 105𝑦 = 0
210𝑥 − 70𝑦 = 280
−175𝑦 = 280
𝑦=
280
175
=
x y 2
 
3 5 7
d)
x y 3
 
2 10 7
𝑥 𝑦 2
+ =
3 5 7
6 1
𝑥= − 𝑦
7 5
6 1
− 𝑦
7 5 +𝑦=2
3
5 7
𝑦=0
6 1
− ×0
7 5
6
𝑥=
7
𝑥=
−56
335
e)
2x  3 y  2
6 x  12 y  1
2𝑥 = −3𝑦 + 2
1
𝑥 = 2 (−3𝑦 + 2)
3
𝑥 = 2𝑦 + 1
1
2
𝑥 = = 0.5
1
3
𝑦 = = 0.3
f)
2( x  4) y 9
 
3
2 2
1
4
x  2 y  (3x  2)  
3
3
1)
2𝑥+8
3
𝑦
9
−2=2
2𝑥 8 𝑦 9
+ − =
3 3 2 2
2𝑥 𝑦 9 8
− = −
3
2 2 3
2𝑥 𝑦 11
− =
3
2
6
2𝑥 1 11
+ =
3 2
6
4𝑥 + 3 11
=
6
6
4𝑥 + 3 = 11
4𝑥 = 8
𝑥=2
𝑥 + 2𝑦 −
3𝑥+2
3
3𝑥+6𝑦−3𝑥+2
3
=
6𝑦 + 2 = −4
6𝑦 = −6
𝑦 = −1
=
−4
3
−4
3
7 x  9 y 2x  4

 15
g)
2
2
5( x  1  y)  25
5(𝑥 − 1 + 𝑦) = 25 (II)
𝑥+𝑦 = 6
𝑥 =6−𝑦
Reemplazar (II) en (I)
7𝑥 − 9𝑦 − 2𝑥 − 4 = −30
5(6 − 𝑦) − 9𝑦 = −26
30 − 5𝑦 − 9𝑦 = −26
56 = 14𝑦
4=𝑦
𝑥=2