Respuestas
Ejercicios hechos por reducción
a)
5x - 2y = 2
x + 2y = 2
5x + x - 2y + 2y = 2 + 2
6x = 4
x = 4/6
x = 2/3
x + 2y = 2
2/3 + 2y = 2
2y = 2 - 2/3
2y = 6/3 - 2/3
2y = 4/3
y = 4/3 / 2
y = 4/6
y = 2/3
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b)
5x - y = 3. (4)
-2x + 4y = -12
20x - 4y = 12
-2x + 4y = -12
20x - 2x - 4y + 4y = 12 - 12
18x = 0
x = 0
5x - y = 3
5(0) - y = 3
0 - y = 3
y = -3
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c)
3x + 5y = 15 (-2)
2x - 3y = -9 (3)
-6x - 10y = -30
6x - 9y = -27
-6x + 6x - 10y - 9y = -30 - 27
-19y = -57
y = 57/19
y = 3
2x - 3y = -9
2x - 3(3) = -9
2x - 9 = -9
2x = -9 + 9
2x = 0
x = 0
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d)
4x + 6y = 2 (3)
6x + 5y = 1 (-2)
12x + 18y = 6
-12x - 10y = -2
12x - 12x + 18y - 10y = 6 - 2
8y = 4
y = 4/8
y = 1/2
4x + 6y = 2
4x + 6(1/2) = 2
4x + 6/2 = 2
4x + 3 = 2
4x = 2 - 3
4x = -1
x = - 1/4
Ejercicios hechos por igualación
a)
3x + 4y = 9
2x + 3y = 7
3x = 9 - 4y
x = (9 - 4y) / 3
2x = 7 - 3y
x = (7 - 3y) / 2
x = x
(9 - 4y) / 3 = (7 - 3y) / 2
(9 - 4y)(2) = (7 - 3y)(3)
18 - 8y = 21 - 9y
18 - 21 = - 9y + 8y
-3 = -y
y = 3
3x + 4y = 9
3x + 4(3) = 9
3x + 12 = 9
3x = 9 - 12
3x = -3
x = -3/3
x = -1
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b)
5x - 3y = 9
-2x + 6y = -2
5x = 9 + 3y
x = (9 + 3y) / 5
-2x + 6y = -2
-2x = -2 - 6y
x = (-2 - 6y) / -2
x = x
(9 + 3y) / 5 = (-2 - 6y) / -2
(9 + 3y)(-2) = (-2 - 6y)(5)
-18 - 6y = -10 - 30y
-18 + 10 = -30y + 6y
-8 = -24y
y = 8/24
y = 1/3
5x - 3y = 9
5x - 3(1/3) = 9
5x - 1 = 9
5x = 9 + 1
5x = 10
x = 10/5
x = 2
Ejercicios hechos por sustitución
a)
-3x + 5y = 3
4x + 2y = -4
4x + 2y = -4
2y = -4 - 4x
y = (- 4 - 4x) / 2
y = -2 - 2x
-3x + 5y = 3
-3x + 5(-2 - 2x) = 3
-3x - 10 - 10x = 3
-13x - 10 = 3
-13x = 3 + 10
-13x = 13
x = 13/-13
x = -1
4x + 2y = -4
4(-1) + 2y = -4
-4 + 2y = -4
2y = 0
y = 0
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b)
4x - 5y = 2
5x + 3y = 21
4x - 5y = 2
4x = 2 + 5y
x = (2 + 5y) / 4
5x + 3y = 21
5{(2 + 5y) / 4} + 3y = 21
(10 + 25y) / 4 + 3y = 21
(10 + 25y + 12y) / 4 = 21
10 + 25y + 12y = 21(4)
10 + 37y = 84
37y = 84 - 10
37y = 74
y = 74/37
y = 2
4x - 5y = 2
4x - 5(2) = 2
4x - 10 = 2
4x = 2 + 10
4x = 12
x = 12/4
x = 3