Sistemas de ecuaciones lineales en dos variables. Aplicaciones
Enviado por D A S I • 14 de Diciembre de 2021 • Tareas • 1.583 Palabras (7 Páginas) • 47 Visitas
[pic 1]
Tarea 8. Sistemas de ecuaciones lineales en dos variables. Aplicaciones.
Entregar los ejercicios impares de toda esta tarea.
Ejercicios sobre sistemas de ecuaciones lineales.
1. 𝑥 = 3 − 4𝑦
3(3 − 4𝑦) − 2𝑦 = −5
9 − 12𝑦 − 2𝑦 = −5
9 − 14𝑦 = −5
−14𝑦 = −14
𝑦 = 1
= 3 − 4𝑦
𝑥 = 3 − 4(1)
𝑥 = −1
3. 2𝑥 = 3 − 3𝑦
3
𝑥 =[pic 2]
2
3
3
− 𝑦 2[pic 3]
3
3 ( −[pic 4]
2
𝑦) − 4𝑦 = 13
2[pic 5]
9 9
− 𝑦 − 4𝑦 = 13 2 2[pic 6][pic 7]
9 17
−[pic 8][pic 9]
2 2
𝑦 = 13
9
2( −[pic 10]
2
17
𝑦) = (13)2[pic 11]
2
9 − 17𝑦 = 26
−17𝑦 = 26 − 9
−17𝑦 = 17
𝑦 = −1
𝑥 =
𝑥 =
3 3
− (−1)[pic 12][pic 13]
2 2
3 3
+[pic 14][pic 15]
2 2
𝑥 = 3
5. 𝑢 = 7 + 𝑣
7 + 𝑣 + 𝑣 = 5
2𝑣 = −2
𝑣 = −1
𝑢 = 7 − 1
𝑢 = 6
7. 𝑥 = −7 + 2𝑦
5(−7 + 2𝑦) + 3𝑦 = −9
−35 + 10𝑦 + 3𝑦 = −9 5(−7 + 2𝑦) + 3𝑦 = −9
−35 + 13𝑦 = −9
13𝑦 = −9 + 35
13𝑦 = 26
𝑦 = 2
𝑥 = −7 + 2(2)
𝑥 = −3
11. {𝑥 + 4𝑦 = 2
𝑥 + 4𝑦 = 6
𝑥 = 2 − 4𝑦
2 − 4𝑦 + 4𝑦 = 6
𝑦 = ∅
13. 𝑥 = 3 − 3
(3 −[pic 16]
8
3
𝑦[pic 17]
4
3
𝑦) +[pic 18]
4
5 11
𝑦 = −[pic 19][pic 20]
6 2
9 9
−[pic 21][pic 22]
8 32
𝑦 +
5 11
𝑦 = −[pic 23][pic 24]
6 2
108 − 27𝑦 + 80𝑦 = −528
108 + 53𝑦 = −528
53𝑦 = −636
𝑦 = −12
3
𝑥 = 3 −
𝑥 = 12
(−12)
4[pic 25]
15 No tiene solución
PAGINA 193
1. {1
[pic 26]
8
𝑥 − 𝑦 = 40 (𝑥 + 𝑦) = 11
1
𝑥 + 𝑦 = 11 ÷[pic 27]
8
𝑥 + 𝑦 = 88
𝑥 = 88 − 𝑦
(88 − 𝑦) − 𝑦 = 40 88 − 2𝑦 = 40
40
−2𝑦 =[pic 28]
88
𝑦 = 24
𝑥 = 88 − 24
𝑥 = 64
3. x + y = 1529
x − y = 101 x + y = 1529 x − y = 101 x + y = 1529 x = 1529 − y x − y = 101 x = 101 + y
1529 − y = 101 + y
2y = 1428
y = 1428/2 = 714 x = 1529 − y
x = 1529 − 714
x = 815
2
5. (𝑥 + 𝑦) = 74[pic 29]
3
3
(x − y) = 9[pic 30]
5
2
(𝑥 + 𝑦) = 74 ( )[pic 31]
3
(𝑥 + 𝑦) = 111
x = 111 – y
3
(𝑥 − 𝑦) = 9 ( )[pic 32]
5
(𝑥 − 𝑦) = 15
𝑥 = 15 + 𝑦
(𝑥 − 𝑦) = 15
111 − 𝑦 = 15 + 𝑦
−𝑦 − 𝑦 = 15 − 111
−2𝑦 = −96
𝑦 = −96/2
𝑦 = 48
𝑥 = 111 − 48
7. ( x − y)/3 = 11
x − y = 11 ∗ (3) x − y = 33
𝑥 = 63
(4/9)x = (
3
𝑦)y[pic 33]
4
4 3
x = 𝑦[pic 34][pic 35]
9 4
3
4x = ([pic 36]
4
27
4x =[pic 37]
4
y)9
y
27
x = ([pic 38]
4
y) 4
27
x = y 16[pic 39]
x − y = 33 27
( y ) − y = 33 16[pic 40]
( 27y − 16y)/16 = 33 27y − 16y = 33(16)
...