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
Respuestas
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 ≧◠◡◠≦.