Question

1. Resuelve cada sistema de ecuaciones lineales empleando el método de sustitución.
a. !
x − y = 14
x + y = 52
b. ! x + y = 50
2x + 4y = 134
c. ! x − 5y = 8
−7x + 8y = 25
d. 3
5m − 2n = 13
m + 3n= 6
e. !
2x + 5y = −24
8x − 3y = 19

Answer 1

Respuesta:

a)

x - y = 14

x + y = 52

x = 14 + y / 1

(14 + y) + y = 52

14 + y + y = 52

2y = 52 - 14

2y = 38

y = 38/2

y = 19

x - y = 14

x - 19 = 14

x = 14 + 19

x = 33

x + y = 52

x + 19 = 52

x = 52 - 19

x = 33

x = 33 ; y = 19

b)

x + y = 50

2x + 4y = 134

x = 50 - y / 1

2 (50 - y) + 4y = 134

100 - 2y + 4y = 134

-2y + 4y = 134 - 100

2y = 34

y = 34/2

y = 17

x + y = 50

x + 17 = 50

x = 50 - 17

x = 33

2x + 4y = 134

2x + 4 (17) = 134

2x + 68 = 134

2x = 134 - 68

2x = 66

x = 66/2

x = 33

x = 33 ; y = 17

c)

x − 5y = 8

−7x + 8y = 25

x = 8 + 5y / 1

-7 (8 + 5y) + 8y = 25

-56 - 35y + 8y = 25

-35y + 8y = 25 + 56

(-) -27y = 81

y = -81/27

y = -3

x − 5y = 8

x - 5(-3) = 8

x - (-15) = 8

x + 15 = 8

x = 8 - 15

x = - 7

−7x + 8y = 25

-7x + 8(-3) = 25

-7x + (-24) = 25

-7x - 24 = 25

-7x = 25 + 24

(-) -7x = 49

x = -49/7

x = -7

x = -7 ; y = -3

d)

5m − 2n = 13

m + 3n = 6

m = 13 + 2n / 5

(13 + 2n / 5) + 3n = 6

13 + 2n = 5 (6 - 3n)

13 + 2n = 30 - 15n

2n + 15n = 30 - 13

17n = 17

n = 17/17

n = 1

5m − 2n = 13

5m - 2(1) = 13

5m - 2 = 13

5m = 13 +2

5m = 15

m = 15/5

m = 3

m + 3n = 6

m + 3(1) = 6

m + 3 = 6

m = 6 - 3

m = 3

m = 3 ; n = 1

e)

2x + 5y = −24

8x − 3y = 19

x = 24 - 5y / 2

8 (24 - 5y / 2) - 3y = 19

4 (24 - 5y) - 3y = 19

96 - 20y - 3y = 19

-20y - 3y = 19 - 96

(-) -23y = -77

y = 77/23 ó 3.35

2x + 5y = −24

2x + 5(3.35) = -24

2x + 16.8 = -24

2x = -24 - 16.8

2x = 7.2

x = 7.2/2

x = 3.6

8x − 3y = 19

8x - 3(3.35) = 19

8x - 10.1 = 19

8x = 19 + 10.1

8x = 29.01

x = 29.01/8

x = 3.6

x = 3.6 ; y = 3.35

Espero haberte ayudado. Suerte en los estudios ≧◠◡◠≦.